Principle of Finite Choice

Theorem
Let $$\mathbb S$$ be a set of sets such that:
 * $$\forall S \in \mathbb S: S \ne \varnothing$$

that is, none of the sets in $$\mathbb S$$ may be empty.

Let $$\mathbb S$$ be finite.

Then there exists a choice function $$f: \mathbb S \to \bigcup \mathbb S$$ defined as:
 * $$\forall S \in \mathbb S: \exists x \in S: f \left({S}\right) = x$$

Thus, if $$\mathbb S$$ is finite, we can construct a choice function on $$\mathbb S$$ by picking one element from each member of $$\mathbb S$$.