Rule of Distribution/Disjunction Distributes over Conjunction/Right Distributive

Theorem

The disjunction operator is right distributive over the conjunction operator:

Formulation 1

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

Formulation 2

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