Let A,B, and C be sets where A is not equal to the empty set. If AXB = AXC, then B=C.

Assume: AxB=AxC

Prove: B=C

Explain where the assumption that A is not equal to the empty set is needed, in the proof.

I know that I must show that B is a subset of C, and C is a subset of B, therefore sense they are subsets of each other they are equal. But I am not sure at all how to show that they are subsets of each other other than basic assumptions. Any help?