Rule of Distribution/Disjunction Distributes over Conjunction

Definition
Disjunction distributes over conjunction:

Disjunction is Right Distributive over Conjunction

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

Alternative rendition
These can alternatively be rendered as:

They can be seen to be logically equivalent to the forms above.

Proof
By the tableau method of natural deduction: