Double Negation/Double Negation Introduction/Sequent Form/Formulation 2

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Theorem

$\vdash p \implies \neg \neg p$


Proof

By the tableau method of natural deduction:

$\vdash p \implies \neg \neg p$
Line Pool Formula Rule Depends upon Notes
1 1 $p$ Assumption (None)
2 1 $\neg \neg p$ Double Negation Introduction: $\neg \neg \mathcal I$ 1
3 $p \implies \neg \neg p$ Rule of Implication: $\implies \mathcal I$ 1 – 2 Assumption 1 has been discharged

$\blacksquare$


Sources