contrapositive

n. Logic
A proposition derived by negating and permuting the terms of another, equivalent proposition; for example, All not-Y is not-X is the contrapositive of All X is Y.

noun

That which is diametrically opposed to another: antipode, antipodes, antithesis, antonym, contrary, converse, counter, opposite, reverse. Logic contradictory. See support/oppose.

The contrapositive of a conditional ‘if If p then q’ is the conditional ‘If not-q then not-p’. The two forms are equivalent. The contrapositive of a generalization ‘all All As are B’ is the equivalent ‘all All non-Bs are non-A’. This equivalence is exploited in Hempel's paradox.