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Theorem hadass 1376
Description: Associative law for triple XOR. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
hadass  |-  (hadd (
ph ,  ps ,  ch )  <->  ( ph \/_ ( ps \/_ ch )
) )

Proof of Theorem hadass
StepHypRef Expression
1 df-had 1370 . 2  |-  (hadd (
ph ,  ps ,  ch )  <->  ( ( ph \/_ ps ) \/_ ch ) )
2 xorass 1299 . 2  |-  ( ( ( ph \/_ ps ) \/_ ch )  <->  ( ph \/_ ( ps \/_ ch ) ) )
31, 2bitri 240 1  |-  (hadd (
ph ,  ps ,  ch )  <->  ( ph \/_ ( ps \/_ ch )
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   \/_wxo 1295  haddwhad 1368
This theorem is referenced by:  hadcomb  1379
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 177  df-xor 1296  df-had 1370
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