I have to prove that if the cardinality of A = the cardinality of B AND the cardinality of C = the cardinality of D then the cardinality of (A x C) = the cardinality of (B x D) with sets A,B,C,D and x denoting the cartesian product.

I know that there exists a bijection f: A to B and a bijection g: C to D. But how do I proceed using this idea of bijections?

Thanks for your help in advance.