Image of Doubleton under Mapping

Theorem
Let $S, T$ be sets.

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

Then $\forall x, y \in S: f\left[{\left\{ {x, y}\right\} }\right] = \left\{ {f\left({x}\right), f\left({y}\right)}\right\}$

Proof
Let $x, y \in S$.

Thus