Modus Ponendo Tollens

Proof Rule
The modus ponendo tollens is a valid deduction sequent in propositional logic: If two statements can not both be true, and one of them is true, it follows that the other one is not true.

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

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

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

Technical Note
When invoking Modus Ponendo Tollens in a tableau proof, use the ModusPonendoTollens template:



or:

where:
 * is the number of the line on the tableau proof where Modus Ponendo Tollens is to be invoked
 * is the pool of assumptions (comma-separated list)
 * is the statement of logic that is to be displayed in the Formula column, without the  delimiters
 * is the first of the two lines of the tableau proof upon which this line directly depends, the one in the form $\neg \left({p \land q}\right)$
 * is the second of the two lines of the tableau proof upon which this line directly depends, the one in the form $p$
 * should hold 1 for, and 2 for
 * is the (optional) comment that is to be displayed in the Notes column.