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

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Theorem

$p \land \paren {p \lor q} \vdash p$


Proof

By the tableau method of natural deduction:

$p \land \paren {p \lor q} \vdash p$
Line Pool Formula Rule Depends upon Notes
1 1 $p \land \paren {p \lor q}$ Premise (None)
2 1 $p$ Rule of Simplification: $\land \mathcal E_1$ 1

$\blacksquare$


Sources