Image of Element under Composite Relation with Common Codomain and Domain

Theorem
Let $\RR_1 \subseteq S \times T$ and $\RR_2 \subseteq T \times U$ be relations.

Let $\RR_2 \circ \RR_1 \subseteq S \times U$ be the composition of $\RR_1$ and $\RR_2$.

Let $x \in S$.

Then:
 * $\RR_2 \sqbrk {\map {\RR_1} x} = \map {\paren{\RR_2 \circ \RR_1}} x$

where $\map {\RR_1} x$ denotes the image of $x$ under $R_1$.