Is


$U_{\omega}=\{x|\forall z((\emptyset\in z\wedge \forall u, v(u,v\in z\rightarrow\{w|w\in u\vee w=u\}\in z))\rightarrow x\in z)\}$


identical with the set $V_{\omega}$ of hereditarily finite sets, i.e. the level $\omega$ of the cumulative hierarchy?