Composite function by definition

I found this expression on Wikipedia:

If , then ,

where and are identity functions.

I wanted to see whether it's true. So I rewrite the expression using the definition of composite function.

Definition:

for , , , and .

I replaced with in and replaced with , where . So I wrote the expression for the LHS

Let and , where and .

, but now my difficulty being that I don't know how to express the RHS

I can't find any information anywhere on the web proving .

Could someone please show me how to write the expression for the RHS?