Rule of Distribution/Disjunction Distributes over Conjunction/Left Distributive

From ProofWiki
Jump to navigation Jump to search

Theorem

The disjunction operator is left distributive over the conjunction operator:

Formulation 1

$p \lor \left({q \land r}\right) \dashv \vdash \left({p \lor q}\right) \land \left({p \lor r}\right)$

Formulation 2

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