Theorem nfxfr

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 11-Aug-2016)

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

Proof

Step	Hyp	Ref	Expression
1		nfbii.1	⊢ ( 𝜑 ↔ 𝜓 )
2		nfxfr.2	⊢ Ⅎ 𝑥 𝜓
3	1	nfbii	⊢ ( Ⅎ 𝑥 𝜑 ↔ Ⅎ 𝑥 𝜓 )
4	2 3	mpbir	⊢ Ⅎ 𝑥 𝜑