DSolve[] and initial conditions

Take some simple function of 2 variables, e.g. f[x_,y_] := x+y and try to solve a PDE of it for the general solution:

DSolve[{Derivative[1,0][f][x,y] == 1, Derivative[0,1][f][x,y] == 1},f,{x,y}]

This works as expected. However, if you try to give an initial condition for a particular solution, MMA is no more able to solve it:

DSolve[{Derivative[1, 0][f][x, y] == 1, 
  Derivative[0, 1][f][x, y] == 1, f[0, 0] == 0}, f, {x, y}]

Has anyone an explanation?