Theorem nfcxfr

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

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

Proof

Step	Hyp	Ref	Expression
1		nfcxfr.1	|- A = B
2		nfcxfr.2	|- F/_ x B
3	1	nfceqi	|- ( F/_ x A <-> F/_ x B )
4	2 3	mpbir	|- F/_ x A