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Theorem dfbi3 903
 Description: An alternate definition of the biconditional. Theorem *5.23 of [WhiteheadRussell] p. 124. (Contributed by NM, 27-Jun-2002.) (Proof shortened by Wolf Lammen, 3-Nov-2013.)
Assertion
Ref Expression
dfbi3

Proof of Theorem dfbi3
StepHypRef Expression
1 xor 901 . 2
2 pm5.18 358 . 2
3 notnot 293 . . . 4
43anbi2i 699 . . 3
5 ancom 452 . . 3
64, 5orbi12i 524 . 2
71, 2, 63bitr4i 281 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 188   wo 370   wa 371 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 This theorem is referenced by:  pm5.24  904  4exmid  949  nanbi  1392  nanbiOLD  1393  nanbiOLDOLD  1394  ifbi  3901  sqf11  24059  bj-dfbi4  31142  raaan2  38590  2reu4a  38604
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