QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  ska6 Unicode version

Theorem ska6 234
Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA6.
Assertion
Ref Expression
ska6 ((a ^ (b ^ c)) == ((a ^ b) ^ c)) = 1

Proof of Theorem ska6
StepHypRef Expression
1 anass 76 . . 3 ((a ^ b) ^ c) = (a ^ (b ^ c))
21ax-r1 35 . 2 (a ^ (b ^ c)) = ((a ^ b) ^ c)
32bi1 118 1 ((a ^ (b ^ c)) == ((a ^ b) ^ c)) = 1
Colors of variables: term
Syntax hints:   = wb 1   == tb 5   ^ wa 7  1wt 8
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
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42
  Copyright terms: Public domain W3C validator