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Metamath Proof Explorer

Theorem nfre1

Description: The setvar x is not free in E. x e. A ph . (Contributed by NM, 19-Mar-1997) (Revised by Mario Carneiro, 7-Oct-2016)

		Ref	Expression
	Assertion	nfre1	$⊢ Ⅎ x \exists x \in A φ$

Step	Hyp	Ref	Expression
1		df-rex	$⊢ \exists x \in A φ \leftrightarrow \exists x (x \in A \land φ)$
2		nfe1	$⊢ Ⅎ x \exists x (x \in A \land φ)$
3	1 2	nfxfr	$⊢ Ⅎ x \exists x \in A φ$