Definition:Natural Deduction/Technical Note

Technical Note
In order to make the use of the proof rules of natural deduction in a tableau proof on, the following templates have been developed:


 * Template:Premise, for using the Rule of Assumption for a premise
 * Template:Assumption, for using the Rule of Assumption for an assumption which is not a premise
 * Template:Conjunction, for using the Rule of Conjunction
 * Template:Simplification, for using the Rule of Simplification
 * Template:Addition, for using the Rule of Addition
 * Template:OrElimination, for using the Rule of Or-Elimination
 * Template:ModusPonens, for using the Modus Ponendo Ponens
 * Template:ModusTollens, for using the Modus Tollendo Tollens
 * Template:ModusPonendoTollens, for using the Modus Ponendo Tollens
 * Template:ModusTollendoPonens, for using the Modus Tollendo Ponens
 * Template:Implication, for using the Rule of Implication
 * Template:DoubleNegIntro, for using Double Negation Introduction
 * Template:DoubleNegElimination, for using Double Negation Elimination
 * Template:BiconditionalIntro, for using Biconditional Introduction
 * Template:BiconditionalElimination, for using Biconditional Elimination
 * Template:NonContradiction, for using the Principle of Non-Contradiction
 * Template:Contradiction, for using Proof by Contradiction
 * Template:BottomElimination, for using the Rule of Bottom-Elimination
 * Template:ExcludedMiddle, for using the Law of Excluded Middle
 * Template:Reductio, for using the Reductio Ad Absurdum

For convenience, other templates are also available, for the following derived rules:


 * Template:Commutation, for using the Rule of Commutation
 * Template:DeMorgan, for using De Morgan's Laws (Logic)
 * Template:Idempotence, for using the Rule of Idempotence
 * Template:IdentityLaw for using the Law of Identity

For the general Rule of Sequent Introduction and Rule of Theorem Introduction, there exist the following templates:


 * Template:SequentIntro
 * Template:TheoremIntro

For the Rule of Substitution, use:
 * Template:Substitution