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Theorem xor 902
 Description: Two ways to express "exclusive or." Theorem *5.22 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 22-Jan-2013.)
Assertion
Ref Expression
xor

Proof of Theorem xor
StepHypRef Expression
1 iman 426 . . . 4
2 iman 426 . . . 4
31, 2anbi12i 703 . . 3
4 dfbi2 634 . . 3
5 ioran 493 . . 3
63, 4, 53bitr4ri 282 . 2
76con1bii 333 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   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:  dfbi3  904  pm5.24  905  4exmid  950  excxor  1411  elsymdif  3668  symdif2  3671  rpnnen2  14278  ist0-3  20361  prtlem90  32431  abnotataxb  38504  ldepslinc  40355
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