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

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## Theorem

- $p \vdash \neg \neg p$

## Proof

By the tableau method of natural deduction:

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 |

$\blacksquare$