Image of Domain of Relation is Image Set

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

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

The image of the domain of $\RR$ is the image set of $\RR$:


 * $\RR \sqbrk {\Dom \RR} = \Img \RR$

where $\Img \RR$ is the image of $\RR$.

Proof
Let $y \in \RR \sqbrk {\Dom \RR}$.

Let $y \in \Img \RR$.

The result follows by definition of set equality.