Theorem nfned

Description: Bound-variable hypothesis builder for inequality. (Contributed by NM, 10-Nov-2007) (Revised by Mario Carneiro, 7-Oct-2016)

	Ref	Expression
Hypotheses	nfned.1	|- ( ph -> F/_ x A )
	nfned.2	|- ( ph -> F/_ x B )
Assertion	nfned	|- ( ph -> F/ x A =/= B )

Proof

Step	Hyp	Ref	Expression
1		nfned.1	|- ( ph -> F/_ x A )
2		nfned.2	|- ( ph -> F/_ x B )
3		df-ne	|- ( A =/= B <-> -. A = B )
4	1 2	nfeqd	|- ( ph -> F/ x A = B )
5	4	nfnd	|- ( ph -> F/ x -. A = B )
6	3 5	nfxfrd	|- ( ph -> F/ x A =/= B )