theorem Th70:
  for H being strict finite Subgroup of G holds card H = 1 implies H = (0).G
proof
  let H be strict finite Subgroup of G;
  assume card H = 1;
  then consider x being object such that
A1: the carrier of H = {x} by CARD_2:42;
  0_G in H by Th46;
  then x = 0_G by A1,TARSKI:def 1;
  hence thesis by A1,Def7;
end;
