Image of Singleton under Mapping

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

Then the image of an element of $S$ is equal to the image of a singleton containing that element, the singleton being a subset of $S$:


 * $\forall s \in S: \set {\map f s} = f \sqbrk {\set s}$

Proof
By definition, a mapping is a relation.

Thus Image of Singleton under Relation applies.