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	⊢ ( 𝜑 → Ⅎ 𝑥 𝐵 )
Assertion	nfcxfrd	⊢ ( 𝜑 → Ⅎ 𝑥 𝐴 )

Proof

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