Rule of Distribution/Conjunction Distributes over Disjunction/Left Distributive

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Theorem

The conjunction operator is left distributive over the disjunction operator:

Formulation 1

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


Formulation 2

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