 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 Th22:
  Conjugate 1_G = id the carrier of G
proof
  for a holds (Conjugate 1_G).a = a
  proof
    let a;
    a |^ 1_G = a by GROUP_3:19;
    hence thesis by Def6;
  end; then
  for q being object st q in the carrier of G holds (Conjugate 1_G).q = q;
  hence thesis;
end;
