Modus Tollendo Ponens

Proof Rule
The modus tollendo ponens is a valid deduction sequent in propositional logic:
 * If either of two statements is true, and one of them is known not to be true, it follows that the other one is true.

It can be written:
 * $\displaystyle {\left({p \lor q}\right) \quad \neg p \over q} \textrm{MTP}_1 \qquad \text{or} \qquad {\left({p \lor q}\right) \quad \neg q \over p} \textrm{MTP}_2$

Variants
The following forms can be used as variants of this theorem:

Variant 2
Note that the form:

requires Law of Excluded Middle.

Therefore it is not valid in intuitionist logic.

Also known as
The modus tollendo ponens is also known as the disjunctive syllogism.

Also see
The following are related argument forms:
 * Modus Ponendo Ponens
 * Modus Ponendo Tollens
 * Modus Tollendo Tollens

Linguistic Note
Modus tollendo ponens is Latin for mode that by denying, affirms.