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

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Theorem

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


Proof

By the tableau method of natural deduction:

$p \vdash p \lor \paren {p \land q} $
Line Pool Formula Rule Depends upon Notes
1 1 $p$ Premise (None)
2 1 $p \lor \paren {p \land q}$ Rule of Addition: $\lor \II_1$ 1

$\blacksquare$


Sources