# Rule of Explosion/Sequent Form

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## Theorem

The Rule of Explosion can be symbolised by the sequent:

- $\bot \vdash \phi$

## Proof

By the tableau method of natural deduction:

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

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

2 | 1 | $\phi$ | Rule of Explosion: $\bot \mathcal E$ | 1 |

$\blacksquare$