Modus Ponendo Tollens/Variant/Formulation 2

Theorem
The modus ponendo tollens is a valid deduction sequent in propositional logic:
 * $\vdash \left({\neg \left({p \land q}\right)}\right) \iff \left({p \implies \neg q}\right)$

That is:
 * If two statements can not both be true, and one of them is true, it follows that the other one is not true.

Its abbreviation in a tableau proof is $\mathrm {MPT}$.

Linguistic Note
Modus ponendo tollens is Latin for mode that by affirming, denies.

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