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Mirrors > Home > QLE Home > Th. List > ska3 | GIF version |
Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA3. (Contributed by NM, 30-Aug-1997.) |
Ref | Expression |
---|---|
ska3 | ((a ≡ b)⊥ ∪ (a⊥ ≡ b⊥ )) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | conb 122 | . . . 4 (a ≡ b) = (a⊥ ≡ b⊥ ) | |
2 | 1 | ax-r4 37 | . . 3 (a ≡ b)⊥ = (a⊥ ≡ b⊥ )⊥ |
3 | 2 | lor 70 | . 2 ((a⊥ ≡ b⊥ ) ∪ (a ≡ b)⊥ ) = ((a⊥ ≡ b⊥ ) ∪ (a⊥ ≡ b⊥ )⊥ ) |
4 | ax-a2 31 | . 2 ((a ≡ b)⊥ ∪ (a⊥ ≡ b⊥ )) = ((a⊥ ≡ b⊥ ) ∪ (a ≡ b)⊥ ) | |
5 | df-t 41 | . 2 1 = ((a⊥ ≡ b⊥ ) ∪ (a⊥ ≡ b⊥ )⊥ ) | |
6 | 3, 4, 5 | 3tr1 63 | 1 ((a ≡ b)⊥ ∪ (a⊥ ≡ b⊥ )) = 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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