Consider the natural numbers $\mathbb{N}$ as a structure for NBG set theory. If we interpret the Axiom of Unions in this structure, we get the statement $(\forall a \in \mathbb{N})$ $(\exists w \in \mathbb{N})$ $(\forall x \in \mathbb{N})$ $((\exists y \in \mathbb{N})(x < y \land y < a) \Rightarrow x < w)$.

Is this statement true? I suspect so: for any $a$, just choose $w = a$. However, Mathematica disagrees with me, and I'm not entirely confident enough with first-order logic to trust myself.