Double Negation/Double Negation Introduction/Sequent Form/Formulation 1/Proof

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Theorem

$p \vdash \neg \neg p$


Proof

By the tableau method of natural deduction:

$p \vdash \neg \neg p$
Line Pool Formula Rule Depends upon Notes
1 1 $p$ Premise (None)
2 2 $\neg p$ Assumption (None)
3 1, 2 $\bot$ Principle of Non-Contradiction: $\neg \mathcal E$ 1, 2
4 1 $\neg \neg p$ Proof by Contradiction: $\neg \mathcal I$ 2 – 3 Assumption 2 has been discharged

$\blacksquare$


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