Contrary theorem

A theorem obtained by replacing the condition and conclusion of a given initial theorem with their negations, and interchanging them.

Comments

A contrary theorem is usually called a contrapositive theorem. Formally such a theorem is of the form: "If not B, then not A", and is obtained by "contraposition" (i.e. by interchanging the conclusion ($B$) and condition ($A$) and replacing each with its negation) from a given theorem: "If A, then B".