reserve G for Group,
  a,b for Element of G,
  m, n for Nat,
  p for Prime;

theorem Th3:
  a |^ n = 1_G implies a" |^ n = 1_G
proof
  assume a |^ n = 1_G;
  then a" |^ n = (1_G)" by GROUP_1:37
          .= 1_G by GROUP_1:8;
  hence thesis;
end;
