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Axiom of Infinity (AIn)

$$\exists y(\exists z(z \in y \wedge \forall t\neg (t \in z)) \wedge \forall x(x \in y \longrightarrow \exists u(u \in y \wedge \forall v(v \in u \longleftrightarrow v = x \vee v \in x)))$$

$$\exists y(\varnothing \in y \wedge \forall x(x \in y \longrightarrow x \cup \{x\} \in y))$$