# Law of Identity/Formulation 2/Proof 1

## Theorem

$\vdash p \implies p$

## Proof

By the tableau method of natural deduction:

$\vdash p \implies p$
Line Pool Formula Rule Depends upon Notes
1 1 $p$ Premise (None)
2 $p \implies p$ Rule of Implication: $\implies \mathcal I$ 1 – 1 Assumption 1 has been discharged

$\blacksquare$

This is the second shortest tableau proof possible.