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 <> {} for x holds x in f"Q iff x in X
  & f.x in Q
proof
  let f be Function of X,Y;
  assume Y <> {};
  then dom f = X by Def1;
  hence thesis by FUNCT_1:def 7;
end;
