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Theorem ska3 232
Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA3. (Contributed by NM, 30-Aug-1997.)
Assertion
Ref Expression
ska3 ((ab) ∪ (ab )) = 1

Proof of Theorem ska3
StepHypRef Expression
1 conb 122 . . . 4 (ab) = (ab )
21ax-r4 37 . . 3 (ab) = (ab )
32lor 70 . 2 ((ab ) ∪ (ab) ) = ((ab ) ∪ (ab ) )
4 ax-a2 31 . 2 ((ab) ∪ (ab )) = ((ab ) ∪ (ab) )
5 df-t 41 . 2 1 = ((ab ) ∪ (ab ) )
63, 4, 53tr1 63 1 ((ab) ∪ (ab )) = 1
Colors of variables: term
Syntax hints:   = wb 1   wn 4  tb 5  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
This theorem is referenced by: (None)
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