Category:Rule of Implication
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This category contains pages concerning Rule of Implication:
The rule of implication is a valid argument in types of logic dealing with conditionals $\implies$.
This includes propositional logic and predicate logic, and in particular natural deduction.
Proof Rule
- If, by making an assumption $\phi$, we can conclude $\psi$ as a consequence, we may infer $\phi \implies \psi$.
- The conclusion $\phi \implies \psi$ does not depend on the assumption $\phi$, which is thus discharged.
Sequent Form
The Rule of Implication can be symbolised by the sequent:
\(\ds \paren {p \vdash q}\) | \(\) | \(\ds \) | ||||||||||||
\(\ds \vdash \ \ \) | \(\ds p \implies q\) | \(\) | \(\ds \) |
Pages in category "Rule of Implication"
The following 9 pages are in this category, out of 9 total.
R
- Rule of Conditional Proof
- Rule of Implication
- Rule of Implication/Also known as
- Rule of Implication/Explanation
- Rule of Implication/Proof Rule
- Rule of Implication/Proof Rule/Tableau Form
- Rule of Implication/Sequent Form
- Rule of Implication/Sequent Form/Proof 1
- Rule of Implication/Sequent Form/Proof by Truth Table