Absorption Laws (Logic)/Disjunction Absorbs Conjunction/Proof 2
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Theorem
- $p \lor \paren {p \land q} \dashv \vdash p$
Proof
| \(\ds p \lor \paren {p \land q}\) | \(=\) | \(\ds \paren {p \land \top} \lor \paren {p \land q}\) | Conjunction with Tautology | |||||||||||
| \(\ds \) | \(=\) | \(\ds p \land \paren {\top \lor q}\) | Conjunction is Left Distributive over Disjunction | |||||||||||
| \(\ds \) | \(=\) | \(\ds p \land \top\) | Disjunction with Tautology | |||||||||||
| \(\ds \) | \(=\) | \(\ds p\) | Conjunction with Tautology |
$\blacksquare$