How to solve this partial differential equation for $f$?

I want Mathematica to solve for the function $ f$ .

$ f$ satisfies the following constraints.

$ \frac{\partial}{\partial x} f(x,y) = y$

$ \frac{\partial}{\partial y} f(x,y) = x$

$ f(0,0)=0$

It would seem obvious that $ f(x,y) = x y$

Yet I cannot coax Mathematica into returning this result.

Here is my attempt. Mathematica just returns it. What am I missing?

DSolve[     {        x == D[f[x, y] , y]      , y == D[f[x, y] , x]      , f[0, 0] == 0     }  , {f[x, y], f[x, y]} , {x, y} ]