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	$$⊢Ⅎx\exists x\in A\phi$$

Proof

Step	Hyp	Ref	Expression
1		df-rex	$$⊢\exists x\in A\phi \leftrightarrow \exists x\left(x\in A\wedge \phi \right)$$
2		nfe1	$$⊢Ⅎx\exists x\left(x\in A\wedge \phi \right)$$
3	1 2	nfxfr	$$⊢Ⅎx\exists x\in A\phi$$