# False Statement implies Every Statement/Formulation 1/Proof 1

## Theorem

$\neg p \vdash p \implies q$

## Proof

By the tableau method of natural deduction:

$\neg p \vdash p \implies q$
Line Pool Formula Rule Depends upon Notes
1 1 $\neg p$ Premise (None)
2 1 $\neg p \lor q$ Rule of Addition: $\lor \mathcal I_1$ 1
3 1 $p \implies q$ Sequent Introduction 2 Rule of Material Implication

$\blacksquare$