reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;

theorem
  for f being Function of X,Y st Y = {} implies X = {} holds f"(f.:X) = X
proof
  let f be Function of X,Y;
  assume Y <> {} or X = {};
  then
A1: dom f = X by Def1;
  then f"(rng f) = X by RELAT_1:134;
  hence thesis by A1,RELAT_1:113;
end;
