 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
  for a holds (Conjugate a) * (Conjugate 1_G) = Conjugate a &
  (Conjugate 1_G) * (Conjugate a) = Conjugate a
proof
  let a;
  Conjugate 1_G = id the carrier of G by Th22;
  hence thesis by FUNCT_2:17;
end;
