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	⊢ Ⅎ 𝑥 𝐵
Assertion	nfcxfr	⊢ Ⅎ 𝑥 𝐴

Proof

Step	Hyp	Ref	Expression
1		nfcxfr.1	⊢ 𝐴 = 𝐵
2		nfcxfr.2	⊢ Ⅎ 𝑥 𝐵
3	1	nfceqi	⊢ ( Ⅎ 𝑥 𝐴 ↔ Ⅎ 𝑥 𝐵 )
4	2 3	mpbir	⊢ Ⅎ 𝑥 𝐴