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Theorem symdif2 3520
 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 3221 . . . 4
2 eldif 3221 . . . 4
31, 2orbi12i 507 . . 3
4 elun 3220 . . 3
5 xor 861 . . 3
63, 4, 53bitr4i 268 . 2
76abbi2i 2464 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 176   wo 357   wa 358   wceq 1642   wcel 1710  cab 2339   cdif 3206   cun 3207 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215 This theorem is referenced by: (None)
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