Modus Tollendo Ponens/Proof Rule

Proof Rule
Modus tollendo ponens is a valid argument in types of logic dealing with disjunctions $\lor$ and negation $\neg$.

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

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

It can be written:
 * $\ds {\paren {\phi \lor \psi} \quad \neg \phi \over \psi} \textrm {MTP}_1 \qquad \text{or} \qquad {\paren {\phi \lor \psi} \quad \neg \psi \over \phi} \textrm {MTP}_2$

Also see

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