Axiom:Axiom of Replacement/Set Theory

Axiom
Let $P \left({y, z}\right)$ be a propositional function, which determines a function.

For any set $S$, there exists a set $x$ such that, for any element $y$ of $S$, if there exists an element $z$ such that $P \left({y, z}\right)$ is true, then such $z$ appear in $x$.


 * $\exists x: \forall y \in S: \left({\exists z: P \left({y, z}\right) \implies \exists z \in x: P \left({y, z}\right)}\right)$