MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  hadrot Unicode version

Theorem hadrot 1396
Description: Rotation law for triple XOR. (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 1394 . 2  |-  (hadd (
ph ,  ps ,  ch )  <-> hadd ( ps ,  ph ,  ch ) )
2 hadcomb 1395 . 2  |-  (hadd ( ps ,  ph ,  ch )  <-> hadd ( ps ,  ch ,  ph ) )
31, 2bitri 241 1  |-  (hadd (
ph ,  ps ,  ch )  <-> hadd ( ps ,  ch ,  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177  haddwhad 1384
This theorem is referenced by:  sadadd2lem2  12890  saddisjlem  12904
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 1311  df-had 1386
  Copyright terms: Public domain W3C validator