Absorption Laws (Logic)/Disjunction Absorbs Conjunction/Forward Implication

Theorem

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

Proof

 * align="right" | 4 ||
 * align="right" | 3
 * $p$
 * $\land \mathcal E_1$
 * 3
 * align="right" | 5 ||
 * align="right" | 1
 * $p$
 * $\lor \mathcal E$
 * 1, 2-2, 3-4
 * }
 * $\lor \mathcal E$
 * 1, 2-2, 3-4
 * }
 * }