= Contrapositive
{title2=$\neg B\to\neg A$}
The contrapositive of a <logical implication> $A\to B$ reverses the direction and applies <logical negation> to both sides: $\neg B\to\neg A$. In <classical propositional logic> they are equivalent, so either can be proved in place of the other. The <contrapositive> of “<divisibility> by four implies being an <even number>” says that a number that is not an <even number> cannot be divisible by four.
In <Intuitionistic propositional logic>, $A\to B$ still implies its <contrapositive>: assumptions $A$ and $\neg B$ would yield $B$ and hence a <contradiction>. The reverse direction is not generally valid. From $\neg B\to\neg A$ and $A$, one obtains only $\neg\neg B$; obtaining $B$ additionally requires <double-negation elimination>.
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