QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  oml2 Unicode version
Theorem oml2 451
Description: Orthomodular law. Kalmbach 83 p. 22.
Hypothesis
Ref Expression
oml2.1 a =< b
Assertion
Ref Expression
oml2 (a v (a' ^ b)) = b
Proof of Theorem oml2
StepHypRef Expression
1 oml 445 . 2 (a v (a' ^ (a v b))) = (a v b)
2 oml2.1 . . . . 5 a =< b
32df-le2 131 . . . 4 (a v b) = b
43lan 77 . . 3 (a' ^ (a v b)) = (a' ^ b)
54lor 70 . 2 (a v (a' ^ (a v b))) = (a v (a' ^ b))
61, 5, 33tr2 64 1 (a v (a' ^ b)) = b
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2  '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  df-le2 131
This theorem is referenced by:  oml3  452  comcom  453  com3i  467  lem4  511  lem4.6.6i4j2  1099
  Copyright terms: Public domain W3C validator