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

theorem
  for x being object
  for f being Function of {x},Y st Y <> {} holds f.:P c= {f.x}
proof let x be object;
  let f be Function of {x},Y;
  f.:P c= rng f by RELAT_1:111;
  hence thesis by Th47;
end;
