Independence of Bivariate Continuos RV's.

By the two definitions of independence for bivariate continuous RVs: (1) F(x,y)=F_X(x)F_Y(y) and
(2) f(x,y)=f_X(x)f_Y(y).
Prove that these two are equivalent. That is: prove that (1) implies (2) and that (2) implies (1).

I tried to differentiate for one and integrate for the other.


TS Contributor
Actually just a few steps: following from the definition

\( F_{X,Y}(x, y) = \Pr\{X \leq x, Y \leq y\} \)

and almost finish the question.