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Theorem nanbi 1393
 Description: Show equivalence between the biconditional and the Nicod version. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Proof shortened by Wolf Lammen, 27-Jun-2020.)
Assertion
Ref Expression
nanbi

Proof of Theorem nanbi
StepHypRef Expression
1 dfbi3 904 . . 3
2 df-or 372 . . 3
3 df-nan 1385 . . . . 5
43bicomi 206 . . . 4
5 nannot 1392 . . . . 5
6 nannot 1392 . . . . 5
75, 6anbi12i 703 . . . 4
84, 7imbi12i 328 . . 3
91, 2, 83bitri 275 . 2
10 nannan 1389 . 2
119, 10bitr4i 256 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wo 370   wa 371   wnan 1384 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 189  df-or 372  df-an 373  df-nan 1385 This theorem is referenced by:  nic-dfim  1552  nic-dfneg  1553
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