Axiom schema of replacement
Reflection

Lévy's reflection principle for ZFC is equivalent to the axiom of replacement, assuming the axiom of infinity. Lévy's principle is as follows:

This is a schema that consists of countably many statements, one for each formula ϕ {\displaystyle \phi }. Here, ϕ M {\displaystyle \phi ^{M}} means ϕ {\displaystyle \phi } with all quantifiers bounded to M {\displaystyle M}, i.e. ϕ {\displaystyle \phi } but with every instance of ∃ x {\displaystyle \exists x} and ∀ x {\displaystyle \forall x} replaced with ∃ (x ∈ V α) {\displaystyle \exists (x\in V_{\alpha })} and ∀ (x ∈ V α) {\displaystyle \forall (x\in V_{\alpha })} respectively.
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