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Theorem symdifass 3703
 Description: Symmetric difference associates. (Contributed by Scott Fenton, 24-Apr-2012.)
Assertion
Ref Expression
symdifass

Proof of Theorem symdifass
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 biass 361 . . . . . . 7
21notbii 298 . . . . . 6
3 xor3 359 . . . . . . . 8
4 notbi 297 . . . . . . . 8
53, 4bitr4i 256 . . . . . . 7
65con1bii 333 . . . . . 6
7 xor3 359 . . . . . 6
82, 6, 73bitr3ri 280 . . . . 5
9 elsymdif 3699 . . . . . 6
109bibi2i 315 . . . . 5
11 elsymdif 3699 . . . . . 6
1211bibi1i 316 . . . . 5
138, 10, 123bitr4i 281 . . . 4
1413notbii 298 . . 3
15 elsymdif 3699 . . 3
16 elsymdif 3699 . . 3
1714, 15, 163bitr4i 281 . 2
1817eqriv 2419 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 188   wceq 1438   wcel 1869   csymdif 3693 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-v 3084  df-dif 3440  df-un 3442  df-symdif 3694 This theorem is referenced by: (None)
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