Lambda calculus : what about the bound variables in substituting expression?
$x$, $y$, and $v$ are variables not (arbitrary) terms. To the extent that it makes sense to say so, the only variable free in $v$ is $v$. There could still be an issue with, say, $M = \lambda v.x$, i.e. $[v/x]\lambda v.x$, but, by assumption, $v$ is not bound in $M$, so this is not a valid case; $v$ is clearly free in $vPQ$.