Theorem nfxfr

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypotheses	nfbii.1	|- ( ph <-> ps )
	nfxfr.2	|- F/ x ps
Assertion	nfxfr	|- F/ x ph

Proof

Step	Hyp	Ref	Expression
1		nfbii.1	|- ( ph <-> ps )
2		nfxfr.2	|- F/ x ps
3	1	nfbii	|- ( F/ x ph <-> F/ x ps )
4	2 3	mpbir	|- F/ x ph