Theorem nfne

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

	Ref	Expression
Hypotheses	nfne.1	|- F/_ x A
	nfne.2	|- F/_ x B
Assertion	nfne	|- F/ x A =/= B

Proof

Step	Hyp	Ref	Expression
1		nfne.1	|- F/_ x A
2		nfne.2	|- F/_ x B
3		df-ne	|- ( A =/= B <-> -. A = B )
4	1 2	nfeq	|- F/ x A = B
5	4	nfn	|- F/ x -. A = B
6	3 5	nfxfr	|- F/ x A =/= B