[QUE/CM-04002]

Let $\Psi$ be a function of $f,g,h,..$ which are in turn functions of   $q$ and $p$. Let $X(q, p)$ be a function   having zero Poisson brackets with $ f,g,h...$. Show that the Poisson  bracket of $\Psi({f,g,h})$ with $X(q,p)$ also vanishes.