 reserve G for Group;
 reserve H for Subgroup of G;
 reserve a, b, c, x, y for Element of G;
 reserve h for Homomorphism of G, G;
 reserve q, q1 for set;

theorem Th7:
  for f1, f2 being Element of Aut G holds f1 * f2 is Element of Aut G
proof
  let f1, f2 be Element of Aut G;
  reconsider f1, f2 as Homomorphism of G, G by Def1;
  f1 is bijective & f2 is bijective by Th4;
  then f1 * f2 is bijective;
  hence thesis by Th4;
end;
