QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  wlem3.1 Unicode version
Theorem wlem3.1 210
Description: Weak analogue to lemma used in proof of Th. 3.1 of Pavicic 1993.
Hypotheses
Ref Expression
wlem3.1.1 (a v b) = b
wlem3.1.2 (b' v a) = 1
Assertion
Ref Expression
wlem3.1 (a == b) = 1
Proof of Theorem wlem3.1
StepHypRef Expression
1 dfb 94 . . 3 (a == b) = ((a ^ b) v (a' ^ b'))
2 wlem3.1.1 . . . . . 6 (a v b) = b
32leoa 123 . . . . 5 (a ^ b) = a
4 oran 87 . . . . . . . 8 (a v b) = (a' ^ b')'
54ax-r1 35 . . . . . . 7 (a' ^ b')' = (a v b)
65, 2ax-r2 36 . . . . . 6 (a' ^ b')' = b
76con3 68 . . . . 5 (a' ^ b') = b'
83, 72or 72 . . . 4 ((a ^ b) v (a' ^ b')) = (a v b')
9 ax-a2 31 . . . 4 (a v b') = (b' v a)
108, 9ax-r2 36 . . 3 ((a ^ b) v (a' ^ b')) = (b' v a)
111, 10ax-r2 36 . 2 (a == b) = (b' v a)
12 wlem3.1.2 . 2 (b' v a) = 1
1311, 12ax-r2 36 1 (a == b) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6   ^ wa 7  1wt 8
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-b 39  df-a 40
This theorem is referenced by:  woml  211  lem3.1  443
  Copyright terms: Public domain W3C validator