Modus Tollendo Tollens

Context
Natural deduction.

Definition
If we can conclude $$p \Longrightarrow q$$, and we can also conclude $$\lnot q$$, then we may infer $$\lnot p$$:

$$p \Longrightarrow q, \lnot q \vdash \lnot p$$

Its abbreviation in a tableau proof is $$\textrm{MTT}$$.

This is sometimes known as: "modus tollens".

Proof
This is proved by the tableau method:

Q.E.D.