Theorem nfneld

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	nfneld.1	|- ( ph -> F/_ x A )
	nfneld.2	|- ( ph -> F/_ x B )
Assertion	nfneld	|- ( ph -> F/ x A e/ B )

Proof

Step	Hyp	Ref	Expression
1		nfneld.1	|- ( ph -> F/_ x A )
2		nfneld.2	|- ( ph -> F/_ x B )
3		df-nel	|- ( A e/ B <-> -. A e. B )
4	1 2	nfeld	|- ( ph -> F/ x A e. B )
5	4	nfnd	|- ( ph -> F/ x -. A e. B )
6	3 5	nfxfrd	|- ( ph -> F/ x A e/ B )