Image of Singleton under Relation

Theorem
Let $\RR \subseteq S \times T$ be a relation.

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 $S$:


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

Proof
We have the definitions:

Finally:
 * $\map \RR s = \RR \sqbrk {\set s}$

by definition of set equality.