Theorem nfbidf 1887

Description: An equality theorem for effectively not free. (Contributed by Mario Carneiro, 4-Oct-2016.)

Hypotheses

Ref	Expression
nfbidf.1
nfbidf.2

Assertion

Ref	Expression
nfbidf

Proof of Theorem nfbidf

Step	Hyp	Ref	Expression
1		nfbidf.1	. . 3
2		nfbidf.2	. . . 4
3	1, 2	albid 1885	. . . 4
4	2, 3	imbi12d 320	. . 3
5	1, 4	albid 1885	. 2
6		df-nf 1617	. 2
7		df-nf 1617	. 2
8	5, 6, 7	3bitr4g 288	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  F/wnf 1616

This theorem is referenced by:  drnf2  2072  dvelimdf  2077  nfcjust  2606  nfceqdf  2614  wl-nfimf1  29978  nfbii2  30567  bj-drnf2v  34329  bj-nfcjust  34426

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