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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
StepHypRef Expression
1 df-or 370 . . 3
2 dfbi3 893 . . 3
3 df-nan 1344 . . . 4
4 nannot 1351 . . . . . 6
5 nannot 1351 . . . . . 6
64, 5anbi12i 697 . . . . 5
76bicomi 202 . . . 4
83, 7imbi12i 326 . . 3
91, 2, 83bitr4i 277 . 2
10 nannan 1348 . 2
119, 10bitr4i 252 1
Colors of variables: wff setvar class
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
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