Rule of Distribution/Conjunction Distributes over Disjunction/Right Distributive

Theorem

The conjunction operator is right distributive over the disjunction operator:

Formulation 1

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

Formulation 2

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