Rule of Distribution/Disjunction Distributes over Conjunction/Left Distributive/Formulation 1/Reverse Implication

Definition

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

Proof

 * align="right" | 12 ||
 * align="right" | 1, 5
 * $p \lor \left({q \land r}\right)$
 * $\lor \mathcal E$
 * 6, 7-8, 9-11
 * align="right" | 13 ||
 * align="right" | 1
 * $p \lor \left({q \land r}\right)$
 * $\lor \mathcal E$
 * 2, 3-4, 5-12
 * $p \lor \left({q \land r}\right)$
 * $\lor \mathcal E$
 * 2, 3-4, 5-12