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	|- ( ph -> F/ x ph )
Assertion	nf5di	|- F/ x ph

Proof

Step	Hyp	Ref	Expression
1		nf5di.1	|- ( ph -> F/ x ph )
2	1	nf5rd	|- ( ph -> ( ph -> A. x ph ) )
3	2	pm2.43i	|- ( ph -> A. x ph )
4	3	nf5i	|- F/ x ph