Theorem nfnel

Description: Bound-variable hypothesis builder for negated membership. (Contributed by David Abernethy, 26-Jun-2011) (Revised by Mario Carneiro, 7-Oct-2016)

	Ref	Expression
Hypotheses	nfnel.1	|- F/_ x A
	nfnel.2	|- F/_ x B
Assertion	nfnel	|- F/ x A e/ B

Proof

Step	Hyp	Ref	Expression
1		nfnel.1	|- F/_ x A
2		nfnel.2	|- F/_ x B
3		df-nel	|- ( A e/ B <-> -. A e. B )
4	1 2	nfel	|- F/ x A e. B
5	4	nfn	|- F/ x -. A e. B
6	3 5	nfxfr	|- F/ x A e/ B