QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  2vwomr2 Unicode version
Theorem 2vwomr2 362
Description: 2-variable WOML rule.
Hypothesis
Ref Expression
2vwomr2.1 (b v (a' ^ b')) = 1
Assertion
Ref Expression
2vwomr2 (a' v (a ^ b)) = 1
Proof of Theorem 2vwomr2
StepHypRef Expression
1 ancom 74 . . . 4 (a ^ b) = (b ^ a)
2 ax-a1 30 . . . . 5 b = b''
3 ax-a1 30 . . . . 5 a = a''
42, 32an 79 . . . 4 (b ^ a) = (b'' ^ a'')
51, 4ax-r2 36 . . 3 (a ^ b) = (b'' ^ a'')
65lor 70 . 2 (a' v (a ^ b)) = (a' v (b'' ^ a''))
7 ancom 74 . . . . . 6 (a' ^ b') = (b' ^ a')
82, 72or 72 . . . . 5 (b v (a' ^ b')) = (b'' v (b' ^ a'))
98ax-r1 35 . . . 4 (b'' v (b' ^ a')) = (b v (a' ^ b'))
10 2vwomr2.1 . . . 4 (b v (a' ^ b')) = 1
119, 10ax-r2 36 . . 3 (b'' v (b' ^ a')) = 1
1211ax-wom 361 . 2 (a' v (b'' ^ a'')) = 1
136, 12ax-r2 36 1 (a' v (a ^ b)) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361
This theorem depends on definitions:  df-a 40
This theorem is referenced by:  2vwomr2a  364  2vwomlem  365
  Copyright terms: Public domain W3C validator