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	$$⊢\phi \leftrightarrow \psi$$
	nfxfrd.2	$$⊢\chi \to Ⅎx\psi$$
Assertion	nfxfrd	$$⊢\chi \to Ⅎx\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfbii.1	$$⊢\phi \leftrightarrow \psi$$
2		nfxfrd.2	$$⊢\chi \to Ⅎx\psi$$
3	1	nfbii	$$⊢Ⅎx\phi \leftrightarrow Ⅎx\psi$$
4	2 3	sylibr	$$⊢\chi \to Ⅎx\phi$$