# 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:

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 |

$\blacksquare$