= Axiom of countable choice
{title2=$A_n\ne\varnothing\ \forall n\Rightarrow\prod_n A_n\ne\varnothing$}
The axiom of countable choice allows one to choose an element from each member of a countable family of nonempty <sets>. It is a restricted form of the <axiom of choice>. In the usual proof that a <countable union of countable sets> is countable, it suffices to choose one enumerating <injection> for each set; if those enumerations are already supplied, that proof requires no further choice.
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