Rule of Idempotence/Disjunction/Formulation 1/Reverse Implication

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Theorem

$p \lor p \vdash p$


Proof

By the tableau method of natural deduction:

$p \lor p \vdash p$
Line Pool Formula Rule Depends upon Notes
1 1 $p \lor p$ Premise (None)
2 2 $p$ Assumption (None)
3 1 $p$ Proof by Cases: $\text{PBC}$ 1, 2 – 2, 2 – 2 Assumptions 2 and 2 have been discharged

$\blacksquare$


Sources