# Rule of Explosion/Sequent Form

## Theorem

The Rule of Explosion can be symbolised by the sequent:

$\bot \vdash \phi$

## Proof

By the tableau method of natural deduction:

$\bot \vdash \phi$
Line Pool Formula Rule Depends upon Notes
1 1 $\bot$ Premise (None)
2 1 $\phi$ Rule of Explosion: $\bot \mathcal E$ 1

$\blacksquare$