theorem Th15:
  for g being Element of G
  holds (phi . 1_A) . g = g
proof
  let g be Element of G;
  (phi . 1_A) = 1_(AutGroup G) by GROUP_6:31
             .= id the carrier of G by AUTGROUP:9;
  hence (phi . 1_A) . g = g;
end;
