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Theorem ska6 234
Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA6. (Contributed by NM, 30-Aug-1997.)
Assertion
Ref Expression
ska6 ((a ∩ (bc)) ≡ ((ab) ∩ c)) = 1

Proof of Theorem ska6
StepHypRef Expression
1 anass 76 . . 3 ((ab) ∩ c) = (a ∩ (bc))
21ax-r1 35 . 2 (a ∩ (bc)) = ((ab) ∩ c)
32bi1 118 1 ((a ∩ (bc)) ≡ ((ab) ∩ 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
This theorem is referenced by: (None)
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