QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  wom5 Unicode version
Theorem wom5 381
Description: Orthomodular law. Kalmbach 83 p. 22.
Hypotheses
Ref Expression
wom5.1 (a =<2 b) = 1
wom5.2 ((b ^ a') == 0) = 1
Assertion
Ref Expression
wom5 (a == b) = 1
Proof of Theorem wom5
StepHypRef Expression
1 wom5.2 . . . . 5 ((b ^ a') == 0) = 1
21wr1 197 . . . 4 (0 == (b ^ a')) = 1
3 ancom 74 . . . . 5 (b ^ a') = (a' ^ b)
43bi1 118 . . . 4 ((b ^ a') == (a' ^ b)) = 1
52, 4wr2 371 . . 3 (0 == (a' ^ b)) = 1
65wlor 368 . 2 ((a v 0) == (a v (a' ^ b))) = 1
7 or0 102 . . 3 (a v 0) = a
87bi1 118 . 2 ((a v 0) == a) = 1
9 wom5.1 . . 3 (a =<2 b) = 1
109wom4 380 . 2 ((a v (a' ^ b)) == b) = 1
116, 8, 10w3tr2 375 1 (a == b) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6   ^ wa 7  1wt 8  0wf 9   =<2 wle2 10
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131
This theorem is referenced by:  wfh1  423  wfh2  424
  Copyright terms: Public domain W3C validator