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 Th3:
  x\y=0.X & y\z=0.X implies x\z=0.X
proof
  assume that
A1: x\y=0.X and
A2: y\z=0.X;
  ((x\z)\(x\y))\(y\z)=0.X by Th1;
  then (x\z)\(x\y)=0.X by A2,Th2;
  hence thesis by A1,Th2;
end;
