Hey pyromania.

What you looking at comes from an area known as an order statistics. If you want to prove the result yourself calculate Min(A,B).

To start you off consider P[Min(A,B)] which is given by P(A > x and B > x) = P(C < x) = P(A > x)P(B > x) [independence] which is equal to [1 - P(A < x)][1 - P(B < x)] and P(A < x) is the CDF for A(x) and the P(B < x) is the CDF of B(x). Now differentiate both sides to get the PDF of C and compare the two.