Weak Catenary Conjecture for differential varieties

Let $V \subseteq \mathbb A^n$ be a positive-dimensional irreducible differential variety, and let $W \subseteq V$ be a zero-dimensional differential subvariety. Weak Catenary Conjecture. There is a proper irreducible differential subvariety $V_1$ of $V$ such that $V_1 \cap W \neq \emptyset$ and $V_1 \not\subseteq W$. This is a weaker form of the Kolchin catenary conjecture and would follow easily from it, but the source states that no proof is known.