# Category:Tableau Proofs

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This category contains pages defining the presentation of the various proof rules of Natural Deduction as they are to appear in tableau proofs.

## Pages in category "Tableau Proofs"

The following 200 pages are in this category, out of 497 total.

(previous page) (next page)### A

- Absorption Laws (Logic)/Conjunction Absorbs Disjunction/Forward Implication
- Absorption Laws (Logic)/Conjunction Absorbs Disjunction/Reverse Implication
- Absorption Laws (Logic)/Disjunction Absorbs Conjunction/Forward Implication
- Absorption Laws (Logic)/Disjunction Absorbs Conjunction/Reverse Implication

### B

- Biconditional as Disjunction of Conjunctions/Formulation 1/Forward Implication
- Biconditional as Disjunction of Conjunctions/Formulation 1/Reverse Implication
- Biconditional as Disjunction of Conjunctions/Formulation 2
- Biconditional as Disjunction of Conjunctions/Formulation 2/Proof 1
- Biconditional Elimination/Proof Rule/Tableau Form
- Biconditional Elimination/Sequent Form
- Biconditional Elimination/Sequent Form/Proof 1
- Biconditional Elimination/Sequent Form/Proof 1/Form 1
- Biconditional Elimination/Sequent Form/Proof 1/Form 2
- Biconditional Equivalent to Biconditional of Negations/Formulation 1/Forward Implication
- Biconditional Equivalent to Biconditional of Negations/Formulation 1/Reverse Implication
- Biconditional Equivalent to Biconditional of Negations/Formulation 2
- Biconditional iff Disjunction implies Conjunction/Formulation 1/Forward Implication
- Biconditional iff Disjunction implies Conjunction/Formulation 1/Reverse Implication
- Biconditional iff Disjunction implies Conjunction/Formulation 2
- Biconditional Introduction/Proof Rule/Tableau Form
- Biconditional Introduction/Sequent Form
- Biconditional Introduction/Sequent Form/Proof 1
- Biconditional is Associative/Formulation 2
- Biconditional is Commutative/Formulation 1
- Biconditional is Commutative/Formulation 1/Proof 1
- Biconditional is Commutative/Formulation 1/Proof 2
- Biconditional is Commutative/Formulation 2
- Biconditional is Reflexive
- Biconditional is Reflexive/Proof 1
- Biconditional is Transitive/Formulation 1
- Biconditional is Transitive/Formulation 1/Proof 1
- Biconditional is Transitive/Formulation 2
- Biconditional with Contradiction
- Biconditional with Contradiction/Proof 1
- Biconditional with Tautology
- Biconditional with Tautology/Proof 1

### C

- Clavius's Law implies Law of Excluded Middle
- Clavius's Law/Formulation 1
- Clavius's Law/Formulation 1/Proof 1
- Clavius's Law/Formulation 1/Proof 2
- Clavius's Law/Formulation 2
- Clavius's Law/Formulation 2/Proof 1
- Clavius's Law/Formulation 2/Proof 2
- Conjunction Equivalent to Negation of Implication of Negative/Formulation 1/Forward Implication
- Conjunction Equivalent to Negation of Implication of Negative/Formulation 1/Reverse Implication
- Conjunction Equivalent to Negation of Implication of Negative/Formulation 2
- Conjunction Equivalent to Negation of Implication of Negative/Formulation 2/Proof 1
- Conjunction implies Disjunction of Conjunctions with Complements
- Conjunction of Disjunction with Negation is Conjunction with Negation
- Conjunction of Disjunctions Consequence
- Conjunction of Disjunctions with Complements implies Disjunction
- Conjunction with Contradiction
- Conjunction with Contradiction/Proof 1
- Conjunction with Law of Excluded Middle
- Conjunction with Negative Equivalent to Negation of Implication/Formulation 1/Forward Implication
- Conjunction with Negative Equivalent to Negation of Implication/Formulation 1/Reverse Implication
- Conjunction with Negative Equivalent to Negation of Implication/Formulation 2
- Conjunction with Negative Equivalent to Negation of Implication/Formulation 2/Forward Implication
- Conjunction with Negative Equivalent to Negation of Implication/Formulation 2/Proof 1
- Conjunction with Negative Equivalent to Negation of Implication/Formulation 2/Reverse Implication
- Conjunction with Tautology
- Conjunction with Tautology/Proof 1
- Constructive Dilemma/Formulation 1
- Constructive Dilemma/Formulation 1/Proof 1
- Constructive Dilemma/Formulation 1/Proof 3
- Constructive Dilemma/Formulation 2
- Constructive Dilemma/Formulation 3
- Contradiction is Negation of Tautology
- Contradiction is Negation of Tautology/Proof 1
- Contradictory Antecedent
- Contradictory Antecedent/Proof 1
- Contradictory Consequent
- Contradictory Consequent/Proof 1

### D

- De Morgan's Laws (Logic)/Conjunction of Negations/Formulation 1/Forward Implication
- De Morgan's Laws (Logic)/Conjunction of Negations/Formulation 1/Reverse Implication
- De Morgan's Laws (Logic)/Conjunction of Negations/Formulation 2
- De Morgan's Laws (Logic)/Conjunction of Negations/Formulation 2/Forward Implication
- De Morgan's Laws (Logic)/Conjunction of Negations/Formulation 2/Proof 1
- De Morgan's Laws (Logic)/Conjunction of Negations/Formulation 2/Reverse Implication
- De Morgan's Laws (Logic)/Conjunction/Formulation 1/Forward Implication
- De Morgan's Laws (Logic)/Conjunction/Formulation 2
- De Morgan's Laws (Logic)/Conjunction/Formulation 2/Proof 1
- De Morgan's Laws (Logic)/Disjunction of Negations/Formulation 1/Forward Implication
- De Morgan's Laws (Logic)/Disjunction of Negations/Formulation 1/Reverse Implication
- De Morgan's Laws (Logic)/Disjunction of Negations/Formulation 2
- De Morgan's Laws (Logic)/Disjunction of Negations/Formulation 2/Proof 1
- De Morgan's Laws (Logic)/Disjunction/Formulation 1/Forward Implication
- De Morgan's Laws (Logic)/Disjunction/Formulation 1/Reverse Implication
- De Morgan's Laws (Logic)/Disjunction/Formulation 2
- De Morgan's Laws (Logic)/Disjunction/Formulation 2/Proof 1
- De Morgan's Laws (Predicate Logic)/Assertion of Existence
- De Morgan's Laws (Predicate Logic)/Assertion of Universality
- De Morgan's Laws (Predicate Logic)/Denial of Existence
- De Morgan's Laws (Predicate Logic)/Denial of Universality
- Deduction Theorem
- Destructive Dilemma/Formulation 1
- Destructive Dilemma/Formulation 1/Proof 1
- Destructive Dilemma/Formulation 1/Proof 2
- Destructive Dilemma/Formulation 2
- Disjunction and Implication
- Disjunction of Conditional and Converse
- Disjunction of Conditional and Converse/Proof 1
- Disjunction of Conjunctions
- Disjunction of Implications
- Disjunction with Contradiction
- Disjunction with Contradiction/Proof 1
- Disjunction with Tautology
- Disjunction with Tautology/Proof 1
- Double Negation Elimination implies Law of Excluded Middle
- Double Negation Elimination implies Law of Excluded Middle/Proof 2
- Double Negation/Double Negation Elimination/Proof Rule/Tableau Form
- Double Negation/Double Negation Elimination/Sequent Form/Formulation 1
- Double Negation/Double Negation Elimination/Sequent Form/Formulation 1/Proof
- Double Negation/Double Negation Elimination/Sequent Form/Formulation 2
- Double Negation/Double Negation Introduction/Proof Rule/Tableau Form
- Double Negation/Double Negation Introduction/Sequent Form/Formulation 1
- Double Negation/Double Negation Introduction/Sequent Form/Formulation 1/Proof
- Double Negation/Double Negation Introduction/Sequent Form/Formulation 2
- Double Negation/Formulation 1
- Double Negation/Formulation 1/Proof 1
- Double Negation/Formulation 2
- Double Negation/Formulation 2/Proof 1

### E

- Equivalences are Interderivable/Forward Implication
- Equivalences are Interderivable/Reverse Implication
- Exclusive Or is Commutative
- Exclusive Or is Commutative/Proof 1
- Exclusive Or with Contradiction
- Exclusive Or with Contradiction/Proof 1
- Exclusive Or with Tautology
- Exclusive Or with Tautology/Proof 1

### F

- Factor Principles/Conjunction on Left/Formulation 1
- Factor Principles/Conjunction on Left/Formulation 1/Proof 1
- Factor Principles/Conjunction on Left/Formulation 1/Proof 2
- Factor Principles/Conjunction on Left/Formulation 2
- Factor Principles/Conjunction on Right/Formulation 1
- Factor Principles/Conjunction on Right/Formulation 1/Proof 1
- Factor Principles/Conjunction on Right/Formulation 1/Proof 2
- Factor Principles/Conjunction on Right/Formulation 2
- Factor Principles/Disjunction on Left/Formulation 1
- Factor Principles/Disjunction on Left/Formulation 1/Proof 1
- Factor Principles/Disjunction on Left/Formulation 1/Proof 2
- Factor Principles/Disjunction on Left/Formulation 2
- Factor Principles/Disjunction on Right/Formulation 1
- Factor Principles/Disjunction on Right/Formulation 1/Proof 1
- Factor Principles/Disjunction on Right/Formulation 1/Proof 2
- Factor Principles/Disjunction on Right/Formulation 1/Proof 3
- Factor Principles/Disjunction on Right/Formulation 2
- False Statement implies Every Statement/Formulation 1
- False Statement implies Every Statement/Formulation 1/Proof 1
- False Statement implies Every Statement/Formulation 2
- False Statement implies Every Statement/Formulation 2/Proof 1
- False Statement implies Every Statement/Formulation 2/Proof 2

### H

- Hypothetical Syllogism/Formulation 1
- Hypothetical Syllogism/Formulation 1/Proof 1
- Hypothetical Syllogism/Formulation 2
- Hypothetical Syllogism/Formulation 2/Proof 1
- Hypothetical Syllogism/Formulation 2/Proof 2
- Hypothetical Syllogism/Formulation 3
- Hypothetical Syllogism/Formulation 3/Proof 1
- Hypothetical Syllogism/Formulation 4
- Hypothetical Syllogism/Formulation 4/Proof 1
- Hypothetical Syllogism/Formulation 4/Proof 2
- Hypothetical Syllogism/Formulation 5
- Hypothetical Syllogism/Formulation 5/Proof 1
- Hypothetical Syllogism/Formulation 5/Proof 2

### I

- Implication Equivalent to Negation of Conjunction with Negative/Formulation 1/Forward Implication
- Implication Equivalent to Negation of Conjunction with Negative/Formulation 1/Reverse Implication
- Implication Equivalent to Negation of Conjunction with Negative/Formulation 2
- Implication Equivalent to Negation of Conjunction with Negative/Formulation 2/Forward Implication
- Implication Equivalent to Negation of Conjunction with Negative/Formulation 2/Proof 1
- Implication Equivalent to Negation of Conjunction with Negative/Formulation 2/Reverse Implication
- Implication is Left Distributive over Conjunction/Formulation 1
- Implication is Left Distributive over Conjunction/Formulation 1/Proof 1
- Implication is Left Distributive over Conjunction/Formulation 2
- Implication is Left Distributive over Conjunction/Formulation 2/Proof 1
- Implication is Left Distributive over Conjunction/Forward Implication/Formulation 1
- Implication is Left Distributive over Conjunction/Forward Implication/Formulation 1/Proof
- Implication is Left Distributive over Conjunction/Forward Implication/Formulation 2
- Implication is Left Distributive over Conjunction/Forward Implication/Formulation 2/Proof
- Implication is Left Distributive over Conjunction/Reverse Implication/Formulation 1
- Implication is Left Distributive over Conjunction/Reverse Implication/Formulation 1/Proof
- Implication is Left Distributive over Conjunction/Reverse Implication/Formulation 2
- Implication is Left Distributive over Conjunction/Reverse Implication/Formulation 2/Proof
- Implication is Left Distributive over Disjunction/Formulation 1/Forward Implication
- Implication is Left Distributive over Disjunction/Formulation 1/Reverse Implication
- Implication is Left Distributive over Disjunction/Formulation 2

### L

- Law of Excluded Middle for Two Variables
- Law of Excluded Middle implies Peirce's Law
- Law of Excluded Middle/Proof Rule/Tableau Form
- Law of Excluded Middle/Sequent Form
- Law of Excluded Middle/Sequent Form/Proof 1
- Law of Excluded Middle/Sequent Form/Proof 3
- Law of Identity/Formulation 1
- Law of Identity/Formulation 1/Proof 1
- Law of Identity/Formulation 2
- Law of Identity/Formulation 2/Proof 1
- Law of Identity/Formulation 2/Proof 3