Axiom of Countable Choice

Let $S$ be a set, let $\mathbb{N}$ denote the natural numbers, and let $(A_m)_{m\in\mathbb{N}}$ be a family of subsets of $S$ such that $A_m$ is nonempty for every $m\in\mathbb{N}$.

Then there exists a sequence $(a_m)_{m\in\mathbb{N}}$ in $S$ such that $a_m\in A_m$ for every $m\in\mathbb{N}$.