Modus Tollendo Tollens/Sequent Form/Proof 2

Theorem

 * $p \implies q, \neg q \vdash \neg p$

Proof

 * align="right" | 4 ||
 * align="right" | 1, 3
 * $q$
 * $\implies \mathcal E$
 * 1, 3
 * ... and derive $q$ ...
 * align="right" | 5 ||
 * align="right" | 1, 2, 3
 * $\bot$
 * $\neg \mathcal E$
 * 2, 4
 * ... and thence derive a contradiction
 * 2, 4
 * ... and thence derive a contradiction