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Theorem symdif2 3763
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 3485 . . . 4
2 eldif 3485 . . . 4
31, 2orbi12i 521 . . 3
4 elun 3644 . . 3
5 xor 891 . . 3
63, 4, 53bitr4i 277 . 2
76abbi2i 2590 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  \cdif 3472  u.cun 3473
This theorem is referenced by:  mbfeqalem  22049
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-dif 3478  df-un 3480
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