Theorem nfdi 1916

Description: Since the converse holds by a1i 11, this inference shows that we can represent a not-free hypothesis with either (inference form) or (deduction form). (Contributed by NM, 17-Aug-2018.) (Proof shortened by Wolf Lammen, 10-Jul-2019.)

Hypothesis

Ref	Expression
nfdi.1

Assertion

Ref	Expression
nfdi

Proof of Theorem nfdi

Step	Hyp	Ref	Expression
1		nfdi.1	. . . 4
2	1	nfrd 1875	. . 3
3	2	pm2.43i 47	. 2
4	3	nfi 1623	1

Syntax hints:  ->wi 4  A.wal 1393  F/wnf 1616

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617