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Metamath Proof Explorer

Theorem axreg2

Description: Axiom of Regularity expressed more compactly. (Contributed by NM, 14-Aug-2003)

		Ref	Expression
	Assertion	axreg2	$⊢ x \in y \to \exists x (x \in y \land \forall z (z \in x \to \neg z \in y))$

Step	Hyp	Ref	Expression
1		ax-reg	$⊢ \exists x x \in y \to \exists x (x \in y \land \forall z (z \in x \to \neg z \in y))$
2	1	19.23bi	$⊢ x \in y \to \exists x (x \in y \land \forall z (z \in x \to \neg z \in y))$