theorem Th40:
  for G being Group, H being strict Subgroup of G holds H is
  maximal implies Phi(G) is Subgroup of H
proof
  let G be Group, H be strict Subgroup of G;
  assume H is maximal;
  then for a be Element of G holds a in Phi(G) implies a in H by Th38;
  hence thesis by GROUP_2:58;
end;
