For any three relations prove the $ (T \circ S) \circ R = T \circ (S \circ R) $

Question

Prove: For any three relations $R \subset W \times X$, $S \subset X \times Y$, and $T \subset Y \times Z$, $(T \circ S) \circ R = T \circ (S \circ R)$.

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Attempted Proof: suppose $ (a,b) \in T \circ (S \circ R)$ then $ \exists (a,x) \in T \wedge (x,b) \in (S \circ R) $.

Since $ (x,b) \in (S \circ R) \exists (x,y) \in S \wedge (y,b) \in R $ and since $ (a,x) \in T \wedge (x,y) \in S \implies (a,y) \in (T \circ S)$ and $(y,b) \in R$

$\therefore (a,b) \in (T \circ S) \circ R = T \circ (S \circ R) $

Is this correct?