Theorem nfxfrd

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	nfbii.1	⊢ ( 𝜑 ↔ 𝜓 )
	nfxfrd.2	⊢ ( 𝜒 → Ⅎ 𝑥 𝜓 )
Assertion	nfxfrd	⊢ ( 𝜒 → Ⅎ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nfbii.1	⊢ ( 𝜑 ↔ 𝜓 )
2		nfxfrd.2	⊢ ( 𝜒 → Ⅎ 𝑥 𝜓 )
3	1	nfbii	⊢ ( Ⅎ 𝑥 𝜑 ↔ Ⅎ 𝑥 𝜓 )
4	2 3	sylibr	⊢ ( 𝜒 → Ⅎ 𝑥 𝜑 )