# Negation of Excluded Middle is False/Form 2

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## Theorem

$\vdash \neg \neg (p \lor \neg p)$

## Proof

By the tableau method of natural deduction:

$\neg\neg (p \lor \neg p)$
Line Pool Formula Rule Depends upon Notes
1 1 $\neg (p \lor \neg p)$ Assumption (None)
2 1 $\bot$ Sequent Introduction 1 Negation of Excluded Middle is False: Form 1
3 $\neg (p \lor \neg p) \implies \bot$ Rule of Implication: $\implies \mathcal I$ 1 – 2 Assumption 1 has been discharged
4 $\neg \neg (p \lor \neg p)$ Sequent Introduction 3 Negation as Implication of Bottom

$\blacksquare$