Proof by induction would work here.

Let be the statement that:

Base case: True.

Inductive step: Assuming is true, it remains to show that is also true, that is:

Modifying it a bit just to see what we're working with:

(I just expanded the '...' a bit and noticed that is 'in' there)

Now we have to show that the right hand side of and are the same.

Simplify and notice that in :

And now it is a matter of simplifying the inside the brackets.