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Theorem symdif2 3701
 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 3446 . . . 4
2 eldif 3446 . . . 4
31, 2orbi12i 523 . . 3
4 elun 3606 . . 3
5 xor 899 . . 3
63, 4, 53bitr4i 280 . 2
76abbi2i 2550 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187   wo 369   wa 370   wceq 1437   wcel 1872  cab 2407   cdif 3433   cun 3434 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-v 3082  df-dif 3439  df-un 3441 This theorem is referenced by:  mbfeqalem  22596
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