Image of Domain of Mapping is Image Set

Theorem
Let $S$ and $T$ be sets.

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

The image of $S$ is the image set of $f$:
 * $f \left[{S}\right] = \operatorname{Im} \left({f}\right)$

Proof
By definition, a mapping is a relation.

Thus Image of Domain of Relation is Image Set applies.