Rule of Distribution/Disjunction Distributes over Conjunction/Left Distributive/Formulation 2/Forward Implication

Theorem

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

Proof
Using a tableau proof for instance 1 of a Gentzen proof system: