 reserve G, A for Group;
 reserve phi for Homomorphism of A,AutGroup(G);

theorem :: TH51
  A, the multMagma of A are_isomorphic
proof
  set G = the multMagma of A;
  ex f being Homomorphism of A,G st f is bijective
  proof
    reconsider f = id A as Function of A,G;
    for a1,a2 being Element of A
    holds f.(a1 * a2) = (f.a1) * (f.a2);

    then reconsider f=id A as Homomorphism of A,G by GROUP_6:def 6;
    take f;
    thus thesis;
  end;
  hence A,G are_isomorphic by GROUP_6:def 11;
end;
