Mapping from Singleton is Injection

Theorem
Let $f: S \to T$ be a mapping.

Let $S$ be a singleton.

Then $f$ is an injection.

Proof
Let $S = \left\{{s}\right\}$.

For $f$ to be an injection, all we need to do is show:
 * $\forall x_1, x_2 \in S: f \left({x_1}\right) = f \left({x_2}\right) \implies x_1 = x_2$.

But as $S$ is a singleton, it follows that $x_1 = x_2 = s$.

Hence the result.