Modus Ponendo Tollens/Proof Rule

Proof Rule
The Modus Ponendo Tollens is a valid deduction sequent in propositional logic.

As a proof rule it is expressed in either of the two forms:
 * $(1): \quad$ If we can conclude $\neg \left({\phi \land \psi}\right)$, and we can also conclude $\phi$, then we may infer $\neg \psi$.
 * $(2): \quad$ If we can conclude $\neg \left({\phi \land \psi}\right)$, and we can also conclude $\psi$, then we may infer $\neg \phi$.

It can be written:
 * $\displaystyle {\neg \left({\phi \land \psi}\right) \quad \phi \over \neg \psi} \textrm{MPT}_1 \qquad \text{or} \qquad {\neg \left({\phi \land \psi}\right) \quad \psi \over \neg \phi} \textrm{MPT}_2$