Axiom:Axiom of Specification/Set Theory/Also presented as

Axiom of Specification: Also presented as
The axiom of specification can also be specified as follows:


 * If $\phi$ is a property (with parameter $p$), then for any $X$ and $p$ there exists a set:
 * $Y = \paren {u \in X: \map \phi {u, p} }$
 * that contains all those $u \in X$ that have the property $\phi$.


 * $\forall X: \forall p: \exists Y: \forall u: \paren {u \in Y \iff \paren {u \in X \land \map \phi {u, p} } }$