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 Th4:
  x\y=0.X implies (x\z)\(y\z)=0.X & (z\y)\(z\x)=0.X
proof
  assume
A1: x\y=0.X;
  ((z\y)\(z\x))\(x\y)=0.X & ((x\z)\(x\y))\(y\z)=0.X by Th1;
  hence thesis by A1,Th2;
end;
