Axiom:Axiom of Choice/Formulation 2

Axiom
Let $\family {X_i}_{i \mathop \in I}$ be an indexed family of sets all of which are non-empty, indexed by $I$ which is also non-empty.

Then there exists an indexed family $\family {x_i}_{i \mathop \in I}$ such that:
 * $\forall i \in I: x_i \in X_i$

That is, the Cartesian product of a non-empty family of sets which are non-empty is itself non-empty.

Also see

 * Equivalence of Formulations of Axiom of Choice