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	$$⊢Ⅎx\forall x\in A\phi$$

Proof

Step	Hyp	Ref	Expression
1		df-ral	$$⊢\forall x\in A\phi \leftrightarrow \forall x\left(x\in A\to \phi \right)$$
2		nfa1	$$⊢Ⅎx\forall x\left(x\in A\to \phi \right)$$
3	1 2	nfxfr	$$⊢Ⅎx\forall x\in A\phi$$