Modus Tollendo Tollens/Sequent Form/Proof 1

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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 Notes
1 1 $p \implies q$ Premise (None)
2 2 $\neg q$ Premise (None)
3 1, 2 $\neg p$ Modus Tollendo Tollens (MTT) 1, 2