Not the best title but I don't know how to better describe it.
So the image of a set is usually written as $f(B)$, my question is, can I use sets in the place of variables in the expression of my mapping?
The reason I'm asking is, I have to show something along the lines of
So I have to show both sides of the inclusion, so to show this I'm thinking of inserting the (supposed)preimage in the function and see if it gives A, but I'm not sure this kind of operation is legal. If not, what would be a general way to do it?