Theorem nfcxfrdf

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by NM, 19-Nov-2020)

	Ref	Expression
Hypotheses	nfcxfrdf.0	|- F/ x ph
	nfcxfrdf.1	|- ( ph -> A = B )
	nfcxfrdf.2	|- ( ph -> F/_ x B )
Assertion	nfcxfrdf	|- ( ph -> F/_ x A )

Proof

Step	Hyp	Ref	Expression
1		nfcxfrdf.0	|- F/ x ph
2		nfcxfrdf.1	|- ( ph -> A = B )
3		nfcxfrdf.2	|- ( ph -> F/_ x B )
4	1 2	nfceqdf	|- ( ph -> ( F/_ x A <-> F/_ x B ) )
5	3 4	mpbird	|- ( ph -> F/_ x A )