Image of Subset 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 $A \subseteq S$.

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

where $\RR_1 \sqbrk A$ denotes the image of $A$ under $R_1$.