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 Th8:
  x\(x\(x\y)) = x\y
proof
  (x\y)\(x\(x\(x\y)))\((x\(x\y))\y) = 0.X by Th1;
  then (x\y)\(x\(x\(x\y)))\0.X = 0.X by Th1;
  then
A1: (x\y)\(x\(x\(x\y))) = 0.X by Th2;
  (x\(x\(x\y)))\(x\y) = 0.X by Th1;
  hence thesis by A1,Def7;
end;
