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Mirrors > Home > QLE Home > Th. List > skr0 | Unicode version |
Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KR0. |
Ref | Expression |
---|---|
skr0.1 | |
skr0.2 |
Ref | Expression |
---|---|
skr0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-a2 31 | . . 3 | |
2 | or0 102 | . . . 4 | |
3 | 2 | ax-r1 35 | . . 3 |
4 | skr0.1 | . . . . . 6 | |
5 | 4 | ax-r4 37 | . . . . 5 |
6 | df-f 42 | . . . . . 6 | |
7 | 6 | ax-r1 35 | . . . . 5 |
8 | 5, 7 | ax-r2 36 | . . . 4 |
9 | 8 | ax-r5 38 | . . 3 |
10 | 1, 3, 9 | 3tr1 63 | . 2 |
11 | skr0.2 | . 2 | |
12 | 10, 11 | ax-r2 36 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wt 8 wf 9 |
This theorem was proved from axioms: ax-a2 31 ax-a5 34 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38 |
This theorem depends on definitions: df-t 41 df-f 42 |
This theorem is referenced by: skmp3 245 wql2lem3 290 wql2lem4 291 id5id0 352 wr5-2v 366 lem3.3.2 1046 wdwom 1104 |
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