Theorem nfcxfrd

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
	nfcxfrd.2	|- ( ph -> F/_ x B )
Assertion	nfcxfrd	|- ( ph -> F/_ x A )

Proof

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