QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  ska3 Unicode version

Theorem ska3 232
Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA3.
Assertion
Ref Expression
ska3 ((a == b)' v (a' == b')) = 1

Proof of Theorem ska3
StepHypRef Expression
1 conb 122 . . . 4 (a == b) = (a' == b')
21ax-r4 37 . . 3 (a == b)' = (a' == b')'
32lor 70 . 2 ((a' == b') v (a == b)') = ((a' == b') v (a' == b')')
4 ax-a2 31 . 2 ((a == b)' v (a' == b')) = ((a' == b') v (a == b)')
5 df-t 41 . 2 1 = ((a' == b') v (a' == b')')
63, 4, 53tr1 63 1 ((a == b)' v (a' == b')) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6  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
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41
  Copyright terms: Public domain W3C validator