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

theorem Th47:
  for x being object
  for f being Function of {x},Y st Y <> {} holds rng f = {f.x}
proof let x be object;
  let f be Function of {x},Y;
  assume Y <> {};
  then dom f = {x} by Def1;
  hence thesis by FUNCT_1:4;
end;
