theorem Th54:
  nat_hom (1).G is bijective
proof
  reconsider H = the multMagma of (1).G as strict normal Subgroup of G by Lm6;
  set g = nat_hom (1).G;
  reconsider G9=G as Group;
A1: the carrier of H = {1_G9} by Def8;
A2: nat_hom (1).G9 is bijective & g is onto by Th53,GROUP_6:65;
  nat_hom (1).G = nat_hom H by Def20
    .= nat_hom (1).G9 by A1,GROUP_2:def 7;
  hence thesis by A2;
end;
