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Theorem hadrot 1497
Description: Rotation law for the adder sum. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
hadrot  |-  (hadd (
ph ,  ps ,  ch )  <-> hadd ( ps ,  ch ,  ph ) )

Proof of Theorem hadrot
StepHypRef Expression
1 hadcoma 1495 . 2  |-  (hadd (
ph ,  ps ,  ch )  <-> hadd ( ps ,  ph ,  ch ) )
2 hadcomb 1496 . 2  |-  (hadd ( ps ,  ph ,  ch )  <-> hadd ( ps ,  ch ,  ph ) )
31, 2bitri 252 1  |-  (hadd (
ph ,  ps ,  ch )  <-> hadd ( ps ,  ch ,  ph ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187  haddwhad 1489
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-xor 1401  df-had 1490
This theorem is referenced by:  had1  1499  sadadd2lem2  14423  saddisjlem  14437
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