reserve x, y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve C for Category;
reserve O for non empty Subset of the carrier of C;
reserve G,H for AddGroup;
reserve V for Group_DOMAIN;

theorem Th28:
  ex x st x in UN & GO x,Trivial-addLoopStr
proof
  reconsider x2 = op2 as Element of UN by Th3;
  reconsider x3 = comp Trivial-addLoopStr as Element of UN by Th3,Th6;
  reconsider u = {} as Element of UN by CLASSES2:56;
  set x1 = {u};
  Extract {} = u;
  then reconsider x4 = Extract {} as Element of UN;
   reconsider x = [x1,x2,x3,x4] as set by TARSKI:1;
  take x;
  thus x in UN by Th1;
  take x1,x2,x3,x4;
  thus x = [x1,x2,x3,x4];
  take Trivial-addLoopStr;
  thus thesis;
end;
