theorem
  (0).G is Abelian
proof
  let a,b be Element of (0).G;
  a in the carrier of (0).G;
  then a in {0_G} by Def7;
  then
A1: a = 0_G by TARSKI:def 1;
  b in the carrier of (0).G;
  then b in {0_G} by Def7;
  hence thesis by A1,TARSKI:def 1;
end;
