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Axiom-Schema of Replacement (ARep)

$$\forall y_1...\forall y_n [\forall x\forall y\forall y' (\varphi(x, y; y_1 ,..., y_n ) \wedge \varphi(x, y' ; y_1 ,..., y_n ) \longrightarrow y= y' ) \longrightarrow \forall u\exists v\forall z(z \in v \longleftrightarrow \exists w(w \in u \wedge \varphi(w, z; y_1 ,..., y_n )))]$$