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 for g being Function of Y,Z st Z <> {} &
  rng f = Y & rng g = Z holds rng(g*f) = Z
proof
  let f be Function of X,Y;
  let g be Function of Y,Z;
  assume Z <> {};
  then dom g = Y by Def1;
  hence thesis by RELAT_1:28;
end;
