contrapositive

Given an implication of the form

$$p⟹q$$

(“p implies q”) the contrapositive of this implication is

$$\mathrm{\neg }q⟹\mathrm{\neg }p$$

(“not q implies not p”).

An implication and its contrapositive are equivalent statements. When proving a theorem, it is often more convenient or more intuitive to prove the contrapositive instead.