reserve x,y for set;

theorem Th3:
  for F being AbGroup, a being Element of F
  ex b being Element of F st a+b = 0.F & b+a = 0.F
proof
  let F be AbGroup, a be Element of F;
  consider b being Element of F such that
A1: a+b = 0.F by ALGSTR_0:def 11;
  take b;
  thus a+b = 0.F by A1;
  thus thesis by A1;
end;
