Can you obtain the same vector by first projectingyonto V, then projecting this vector onxas by projectingydirectly onxor more generally , if $\displaystyle V$ is a subspace and $\displaystyle V_1$ is a subspace of $\displaystyle V$, does $\displaystyle p(p(\textbf{y}|V)|V_1) = p(\textbf{y}|V_1)$

From the way the question is phrased it seems like its true, but I was wondering if there was an intuitive explanation as to why.