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	$$⊢\phi \leftrightarrow \psi$$
	nfxfr.2	$$⊢Ⅎx\psi$$
Assertion	nfxfr	$$⊢Ⅎx\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfbii.1	$$⊢\phi \leftrightarrow \psi$$
2		nfxfr.2	$$⊢Ⅎx\psi$$
3	1	nfbii	$$⊢Ⅎx\phi \leftrightarrow Ⅎx\psi$$
4	2 3	mpbir	$$⊢Ⅎx\phi$$