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

theorem
  for f,g being Function of X,X st g*f = f & rng f = X holds g = id X
proof
  let f,g be Function of X,X;
  dom g = X by Th51;
  hence thesis by FUNCT_1:23;
end;
