Rule of Transposition/Variant 1/Formulation 1/Forward Implication

Theorem

$p \implies \neg q \vdash q \implies \neg p$

Proof

By the tableau method of natural deduction:

$p \implies \neg q \vdash q \implies \neg p$

Line		Pool	Formula	Rule	Depends upon	Notes
1		1	$p \implies \neg q$	Premise	(None)
2		2	$q$	Assumption	(None)
3		2	$\neg \neg q$	Double Negation Introduction: $\neg \neg \II$	2
4		1, 2	$\neg p$	Modus Tollendo Tollens (MTT)	1, 3
5		1	$q \implies \neg p$	Rule of Implication: $\implies \II$	2 – 4	Assumption 2 has been discharged

$\blacksquare$