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 $S$:


 * $\forall s \in S: \left\{{f \left({s}\right)}\right\} = f \left[{\left\{{s}\right\}}\right]$

Proof
By definition, a mapping is a relation.

Thus Image of Singleton under Relation applies.