Theorem nf5di

Description: Since the converse holds by a1i , this inference shows that we can represent a not-free hypothesis with either F/ x ph (inference form) or ( ph -> F/ x ph ) (deduction form). (Contributed by NM, 17-Aug-2018) (Proof shortened by Wolf Lammen, 10-Jul-2019)

	Ref	Expression
Hypothesis	nf5di.1	$$⊢\phi \to Ⅎx\phi$$
Assertion	nf5di	$$⊢Ⅎx\phi$$

Proof

Step	Hyp	Ref	Expression
1		nf5di.1	$$⊢\phi \to Ⅎx\phi$$
2	1	nf5rd	$$⊢\phi \to \left(\phi \to \forall x\phi \right)$$
3	2	pm2.43i	$$⊢\phi \to \forall x\phi$$
4	3	nf5i	$$⊢Ⅎx\phi$$