Countable Set has Choice Function

Theorem
Let $S$ be a countable set.

Let $\mathbb S = \powerset S \setminus \set \O$ be the power set of $S$ excluding the empty set $\O$.

Then there exists a choice function $C$ for $S$:
 * $\forall x \in \mathbb S: \map C x \in x$

Proof
From Countable Set is Well-Orderable, we have that $S$ is a well-orderable set.

The result follows from Well-Orderable Set has Choice Function.