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Theorem symdif2 3607
 Description: Two ways to express symmetric difference. (Contributed by NM, 17-Aug-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
symdif2
Distinct variable groups:   ,   ,

Proof of Theorem symdif2
StepHypRef Expression
1 eldif 3330 . . . 4
2 eldif 3330 . . . 4
31, 2orbi12i 508 . . 3
4 elun 3488 . . 3
5 xor 862 . . 3
63, 4, 53bitr4i 269 . 2
76abbi2i 2547 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wo 358   wa 359   wceq 1652   wcel 1725  cab 2422   cdif 3317   cun 3318 This theorem is referenced by:  mbfeqalem  19534 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-dif 3323  df-un 3325
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