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Theorem xorass 1317
 Description: is associative. (Contributed by FL, 22-Nov-2010.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Assertion
Ref Expression
xorass

Proof of Theorem xorass
StepHypRef Expression
1 biass 349 . . . . . 6
21notbii 288 . . . . 5
3 nbbn 348 . . . . 5
4 pm5.18 346 . . . . . 6
54con2bii 323 . . . . 5
62, 3, 53bitr4i 269 . . . 4
7 df-xor 1314 . . . . 5
87bibi1i 306 . . . 4
9 df-xor 1314 . . . . 5
109bibi2i 305 . . . 4
116, 8, 103bitr4i 269 . . 3
1211notbii 288 . 2
13 df-xor 1314 . 2
14 df-xor 1314 . 2
1512, 13, 143bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wxo 1313 This theorem is referenced by:  hadass  1395 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 178  df-xor 1314
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