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Mirrors > Home > QLE Home > Th. List > ska10 | GIF version |
Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA10. (Contributed by NM, 30-Aug-1997.) |
Ref | Expression |
---|---|
ska10 | ((a ∪ b)⊥ ≡ (a⊥ ∩ b⊥ )) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oran 87 | . . 3 (a ∪ b) = (a⊥ ∩ b⊥ )⊥ | |
2 | 1 | con2 67 | . 2 (a ∪ b)⊥ = (a⊥ ∩ b⊥ ) |
3 | 2 | bi1 118 | 1 ((a ∪ b)⊥ ≡ (a⊥ ∩ b⊥ )) = 1 |
Colors of variables: term |
Syntax hints: = wb 1 ⊥ wn 4 ≡ tb 5 ∪ 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 df-t 41 df-f 42 |
This theorem is referenced by: ska2 432 |
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