Scope of Quantified Variables in the Axiom of Separation in ZF

Question

I realize in the axiom of separation $$x\in A \leftrightarrow \phi(x)\wedge x\in B$$ the free variable $x$ is restricted to $B$ to avoid Russell's Paradox, but are the quantified variables in $\phi$ bounded by anything? In all of the formulations of the axiom I've seen, no specification has been made, except when a few of the variables are used to define a set with parameters. My question is, if there are variables in $\phi$ which can potentially be any element in the structure (which in the case of set theory is a set since all elements are themselves sets), what prevents them from assuming the value of $A$, the set which is being defined? While it may not be a direct case of a circular definition, I would think it could still lead to inconsistencies- almost of the same variety of Russell's Paradox.