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Axiom of Regularity (AReg)

$$\forall x(\exists y(y \in x) \longrightarrow \exists z(z \in x \wedge \forall u\neg (u \in z \wedge u \in x))$$

$$\forall x(x \neq \varnothing \longrightarrow \exists z(z \in x \wedge (z \cap x = \varnothing)))$$