theorem Th17:
  1_(semidirect_product (G, A, phi)) = <* 1_G, 1_A *>
proof
  reconsider e = <* 1_G, 1_A *> as Element of semidirect_product (G, A, phi)
  by Th9;
  for x being Element of semidirect_product (G, A, phi)
  holds x * e = x & e * x = x by Lm4;
  hence thesis by GROUP_1:def 4;
end;
