Biconditional as Disjunction of Conjunctions

From ProofWiki
Jump to navigation Jump to search

Theorem

Formulation 1

$p \iff q \dashv \vdash \paren {p \land q} \lor \paren {\neg p \land \neg q}$

Formulation 2

$\vdash \paren {p \iff q} \iff \paren {\paren {p \land q} \lor \paren {\neg p \land \neg q} }$


Also known as

This rule is also sometimes included as another form of the Rule of Material Equivalence