Definition:Restricted Existential Quantifier

Definition
Let $A$ be a class in ZF.

The restricted existential quantifier is denoted $\exists x \in A$ and is defined as the following definitional abbreviation:


 * $\exists x \in A: P \left({x}\right) \quad \text{for} \quad \exists x: \left({x \in A \land P \left({x}\right)}\right)$

where $P \left({x}\right)$ is any well-formed formula of the language of set theory.