Absorption Laws (Logic)/Conjunction Absorbs Disjunction/Proof 2

$p \land \paren {p \lor q} \dashv \vdash p$
 $\ds p \land \paren {p \lor q}$ $=$ $\ds \paren {p \lor \bot} \land \paren {p \lor q}$ Disjunction with Contradiction $\ds$ $=$ $\ds p \lor \paren {\bot \land q}$ Disjunction is Left Distributive over Conjunction $\ds$ $=$ $\ds p \lor \bot$ Conjunction with Contradiction $\ds$ $=$ $\ds p$ Disjunction with Contradiction
$\blacksquare$