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Metamath Proof Explorer

Theorem elexOLD

Description: Obsolete version of elex as of 28-May-2025. (Contributed by NM, 26-May-1993) (Proof shortened by Andrew Salmon, 8-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	elexOLD	$⊢ A \in B \to A \in V$

Proof

Step	Hyp	Ref	Expression
1		exsimpl	$⊢ \exists x (x = A \land x \in B) \to \exists x x = A$
2		dfclel	$⊢ A \in B \leftrightarrow \exists x (x = A \land x \in B)$
3		isset	$⊢ A \in V \leftrightarrow \exists x x = A$
4	1 2 3	3imtr4i	$⊢ A \in B \to A \in V$