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Mirrors > Home > QLE Home > Th. List > ska8 | Unicode version |
Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA8. |
Ref | Expression |
---|---|
ska8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | an0 108 | . . . . 5 | |
2 | 1 | ax-r1 35 | . . . 4 |
3 | ancom 74 | . . . 4 | |
4 | 2, 3 | ax-r2 36 | . . 3 |
5 | dff 101 | . . . 4 | |
6 | ancom 74 | . . . 4 | |
7 | 5, 6 | ax-r2 36 | . . 3 |
8 | 7 | ran 78 | . . 3 |
9 | 4, 7, 8 | 3tr2 64 | . 2 |
10 | 9 | bi1 118 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 tb 5 wa 7 wt 8 wf 9 |
This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-a4 33 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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