I have a problem with a simple conditional probability proof. Been working through it for a couple hours but couldn't make any inroads.

$\displaystyle {\text{given that A and B are independent }} \hfill \\P\left( {A,B} \right) = P\left( A \right)P(B) \hfill \\{\text{Prove that}} \hfill \\P\left( {A|B,C} \right) = P(A|C) \hfill \\$