reserve X for set;
reserve G for Group;
reserve H for Subgroup of G;
reserve h,x,y for object;
reserve f for Endomorphism of G;
reserve phi for Automorphism of G;

theorem Th26:
  for G being strict Group, f being object
  holds f in Aut G iff f is Automorphism of G
proof
  let G be strict Group;
  let f be object;
  thus f in Aut G implies f is Automorphism of G
  proof
    assume A1: f in Aut G;
    then reconsider f as Endomorphism of G by AUTGROUP:def 1;
    f is bijective by A1,AUTGROUP:def 1;
    hence thesis;
  end;
  thus f is Automorphism of G implies f in Aut G by AUTGROUP:def 1;
end;
