Definition (Bounded quantifier). We call a quantifier of the form $\exists x\in y,\phi$ or $\forall x\in y,\phi$ a bounded quantifier.

(Defined by $\exists x\in y,\phi :=\exists x(x\in y\wedge \phi )$ and $\forall x\in y\phi :=\forall x(x\in y\to \phi )$).