Modus Tollendo Tollens/Sequent Form/Proof 1

Theorem

The Modus Tollendo Tollens can be symbolised by the sequent:

$\ds p$

$\implies$

$\ds q$

$\ds \neg q$

$\ds $

$\ds \vdash \ \ $

$\ds \neg p$

$\ds $

By the tableau method of natural deduction:

$p \implies q, \neg q \vdash \neg p$
Line	Pool	Formula	Rule	Depends upon
1	1	$p \implies q$	Premise	(None)
2	2	$\neg q$	Premise	(None)
3	1, 2	$\neg p$	Modus Tollendo Tollens (MTT)	1, 2

$\blacksquare$

1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $2$ Conditionals and Negation: Theorem $5$