Composite Relations

Hi all! I'm trying to prove:

Domain(S COMPOSITE R) is a subset of Domain(R)

With R being a relation from a set A to a set B and S being a relation from set B to a set C.

I need to establish that for any element, say x, belonging to

Domain(S COMPOSITE R), it also belongs to Domain(R).

It's easy to verify the claim with a few examples...

Here's one example...

Let A = { 1, 2, 3 }

Let B = { 3, 5, 6 }

Let C = { 7, 8, 9 }

Let R be a relation from A to B

So, R is a subset of A CROSS B

Let R = { (1,3), (2,5), (3,3) }

Let S be a relation from B to C

So, S is a subset of B CROSS C

Let S = { (3,8), (3,9), (6,8) }

Then, S COMPOSITE R = { (1,8), (1,9), (3,8), (3,9) }

So, we have that

Dom(S COMPOSITE R) = { 1, 3 }

and

Dom(R) = { 1, 2, 3 }

Therefore, clearly we see that Domain(S COMPOSITE R) is a subset of Domain(R)
in this example.

How do I prove this in general?

Thanks!