# Proof by Contradiction/Sequent Form

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## Theorem

The Proof by Contradiction can be symbolised by the sequent:

- $\paren {p \vdash \bot} \vdash \neg p$

## Proof

By the tableau method of natural deduction:

Line | Pool | Formula | Rule | Depends upon | Notes | |
---|---|---|---|---|---|---|

1 | 1 | $p \vdash \bot$ | Premise | (None) | ||

2 | 2 | $p$ | Assumption | (None) | ||

3 | 1 | $\neg p$ | Proof by Contradiction: $\neg \II$ | 2 – 2 | Assumption 2 has been discharged |

$\blacksquare$