Modus Tollendo Tollens/Sequent Form/Proof 2

Theorem
The modus tollendo tollens (or modus tollens) is a valid deduction sequent in propositional logic:


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

That is:
 * If the truth of one statement implies the truth of a second, and the second is shown not to be true, then neither can the first.

It can be written:
 * $\displaystyle {p \implies q \quad \neg q \over \neg p} \text{MTT}$

Proof
By the tableau method of natural deduction: