Theorem nanbi 1352

Description: Show equivalence between the biconditional and the Nicod version. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Proof shortened by Wolf Lammen, 9-Mar-2020.)

Assertion

Ref	Expression
nanbi

Proof of Theorem nanbi

Step	Hyp	Ref	Expression
1		df-or 370	. . 3
2		dfbi3 893	. . 3
3		df-nan 1344	. . . 4
4		nannot 1351	. . . . . 6
5		nannot 1351	. . . . . 6
6	4, 5	anbi12i 697	. . . . 5
7	6	bicomi 202	. . . 4
8	3, 7	imbi12i 326	. . 3
9	1, 2, 8	3bitr4i 277	. 2
10		nannan 1348	. 2
11	9, 10	bitr4i 252	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  -/\wnan 1343

This theorem is referenced by:  nic-dfim  1502  nic-dfneg  1503

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-nan 1344