I am trying to prove that
A is a subset of B
if and only if
the intersection of A and B is the set A.
It it seems obvious from the definitons but I am having trouble formalizing the proof.
In the forward direction, we know an element x in A implies x in B, and that the intersection of A and B is just all the elements y such that y is in A AND y is in B...
So it seems obvious to me that A intersection B is just A, but how can I state it formally? Similarily for the backwards direction.