I'll quote this from the Wikipedia on Scott-Potter set theory:
Reflection: Let $\Phi$ denote a first-order formula in which any number of free variables are present. Let $\Phi^{(V)}$ denote $\Phi$ with these free variables all quantified, with the quantified variables restricted to the level $V$. Then: $\exists V [\Phi \to \Phi^{(V)}]$
What does it mean to say that all the free variables of $\Phi$ are quantified in $\Phi^{(V)}$? Does it mean that we have $(\bigwedge \exists x_i \in V: x_i=v_i)$ as a subformula of $\Phi^{(V)}$, where $\vec{v}$ is the string of all free variables of $\Phi$?