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Theorem symdifxor 3203
 Description: Expressing symmetric difference with exclusive-or or two differences. (Contributed by Jim Kingdon, 28-Jul-2018.)
Assertion
Ref Expression
symdifxor
Distinct variable groups:   ,   ,

Proof of Theorem symdifxor
StepHypRef Expression
1 eldif 2927 . . . 4
2 eldif 2927 . . . 4
31, 2orbi12i 681 . . 3
4 elun 3084 . . 3
5 excxor 1269 . . . 4
6 ancom 253 . . . . 5
76orbi2i 679 . . . 4
85, 7bitri 173 . . 3
93, 4, 83bitr4i 201 . 2
109abbi2i 2152 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 97   wo 629   wceq 1243   wxo 1266   wcel 1393  cab 2026   cdif 2914   cun 2915 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-xor 1267  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-dif 2920  df-un 2922 This theorem is referenced by: (None)
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