Modus Tollendo Tollens/Proof Rule

Proof Rule
Modus tollendo tollens is a valid argument in types of logic dealing with conditionals $\implies$ and negation $\neg$.

This includes propositional logic and predicate logic, and in particular natural deduction.

As a proof rule it is expressed in the form:
 * If we can conclude $\phi \implies \psi$, and we can also conclude $\neg \psi$, then we may infer $\neg \phi$.

It can be written:
 * $\ds {\phi \implies \psi \quad \neg \psi \over \neg \phi} \text{MTT}$

Also see

 * This is a rule of inference of the following proof systems:
 * Definition:Natural Deduction