Distinguishing between two probabilities and the uniform probability Say I have a polynomial adversary $A$ that can distinguish with a non-negligible adventage between $x$ generated from a probability $X$ and $y$ generated from a probability $Y$.

Obviously, this implies that it is possible to either efficiently distinguish between $X$ and the uniform distribution, or between $Y$ and the uniform distribution (or both).

How can this be proven? 

Can $A$ be directly used to construct another adversary that distinguishes between $X$ and uniform (or $Y$ and uniform) ?
Perhaps a proof by contradiction? Either they are both indistinguishable from uniform or not. If so, they are indistinguishable from each other. Since that contradicts the premise, at least one must be distinguishable from uniform.