# True Statement is implied by Every Statement/Formulation 2/Proof 1

## Theorem

$\vdash q \implies \paren {p \implies q}$

## Proof

By the tableau method of natural deduction:

$\vdash q \implies \paren {p \implies q}$
Line Pool Formula Rule Depends upon Notes
1 1 $q$ Assumption (None)
2 1 $p \implies q$ Sequent Introduction 1 True Statement is implied by Every Statement: Formulation 1
3 $q \implies \paren {p \implies q}$ Rule of Implication: $\implies \mathcal I$ 1 – 2 Assumption 1 has been discharged

$\blacksquare$