False Statement implies Every Statement/Formulation 2/Proof 2

Theorem

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

Proof

By the tableau method of natural deduction:

$\vdash \neg p \implies \left({p \implies q}\right)$

Line		Pool	Formula	Rule	Depends upon	Notes
1		1	$\neg p$	Assumption	(None)
2		1	$p \implies q$	Sequent Introduction	1	False Statement implies Every Statement: Formulation 1
3			$\neg p \implies \left({p \implies q}\right)$	Rule of Implication: $\implies \II$	1 – 2	Assumption 1 has been discharged

$\blacksquare$