reserve X for BCI-algebra;
reserve x,y,z,u,a,b for Element of X;
reserve IT for non empty Subset of X;

theorem Th2:
  x \ 0.X = x
proof
  (x\(x\0.X))\0.X = 0.X by Th1;
  then
A1: x\(x\0.X) = 0.X by Lm1;
  0.X = (x\(x\x))\x by Th1
    .= (x\0.X)\x by Def5;
  hence thesis by A1,Def7;
end;
