QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  oml Unicode version
Theorem oml 445
Description: Orthomodular law. Compare Th. 1 of Pavicic 1987.
Assertion
Ref Expression
oml (a v (a' ^ (a v b))) = (a v b)
Proof of Theorem oml
StepHypRef Expression
1 omlem1 127 . 2 ((a v (a' ^ (a v b))) v (a v b)) = (a v b)
2 omlem2 128 . 2 ((a v b)' v (a v (a' ^ (a v b)))) = 1
31, 2lem3.1 443 1 (a v (a' ^ (a v b))) = (a v b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42
This theorem is referenced by:  omln  446  oml5  449  oml2  451  ud1lem2  561  ud2lem2  564  ud3lem2  571  ud4lem2  582  ud5lem3  594  test  802  2oalem1  825  oas  925  oat  927  lem4.6.6i2j4  1095
  Copyright terms: Public domain W3C validator