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

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## Theorem

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

## Proof

 $\displaystyle p \lor \left({p \land q}\right)$ $=$ $\displaystyle \left({p \land \top}\right) \lor \left({p \land q}\right)$ Conjunction with Tautology $\displaystyle$ $=$ $\displaystyle p \land \left({\top \lor q}\right)$ Conjunction is Left Distributive over Disjunction $\displaystyle$ $=$ $\displaystyle p \land \top$ Disjunction with Tautology $\displaystyle$ $=$ $\displaystyle p$ Conjunction with Tautology

$\blacksquare$