How to show $(T \circ S) \circ R=T \circ (S \circ R)$?

Question

I am a bit new to computer mathematics, and therefore struggle a bit to understand the process of proving the equality in relation sets like this. I can both see and understand that it is correct, but find it hard to prove it in a good and correct way.

The following information is also relevant to the task: $R \subseteq A \times B$, $S \subseteq B \times C$ and $T \subseteq C \times D$.

Thanks!

Answer 1

x((RoS)oT)y
iff exists b with x(RoS)b and bTy
iff exists a,b with xRa, aSb, and bTy
iff exists a with xRa and a(SoT)y
iff x(Ro(SoT))y