= Converse implication
{title2=$B\to A$}
= Converse of an implication
{synonym}
The converse implication of $A\to B$ is $B\to A$. It exchanges hypothesis and conclusion without <logical negation>. It need not follow from the original <logical implication>: $n=2$ is an <even number> but is not divisible by four. Thus “being an <even number> implies <divisibility> by four” is false, although the original implication holds for all <natural numbers>. Proving both directions establishes an “if and only if” statement; proving a <contrapositive> establishes the original implication classically, without establishing its <converse implication>.
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