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Metamath Proof Explorer

Theorem nfra1

Description: The setvar x is not free in A. x e. A ph . (Contributed by NM, 18-Oct-1996) (Revised by Mario Carneiro, 7-Oct-2016)

		Ref	Expression
	Assertion	nfra1	$⊢ Ⅎ x \forall x \in A φ$

Step	Hyp	Ref	Expression
1		df-ral	$⊢ \forall x \in A φ \leftrightarrow \forall x (x \in A \to φ)$
2		nfa1	$⊢ Ⅎ x \forall x (x \in A \to φ)$
3	1 2	nfxfr	$⊢ Ⅎ x \forall x \in A φ$