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Metamath Proof Explorer

Theorem nfreu1

Description: The setvar x is not free in E! x e. A ph . (Contributed by NM, 19-Mar-1997)

		Ref	Expression
	Assertion	nfreu1	$⊢ Ⅎ x \exists! x \in A φ$

Step	Hyp	Ref	Expression
1		df-reu	$⊢ \exists! x \in A φ \leftrightarrow \exists! x (x \in A \land φ)$
2		nfeu1	$⊢ Ⅎ x \exists! x (x \in A \land φ)$
3	1 2	nfxfr	$⊢ Ⅎ x \exists! x \in A φ$