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.