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Mirrors > Home > QLE Home > Th. List > ska15 | Unicode version |
Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA15. |
Ref | Expression |
---|---|
ska15 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-i3 46 | . . 3 | |
2 | ax-a2 31 | . . . . . 6 | |
3 | lea 160 | . . . . . . 7 | |
4 | lear 161 | . . . . . . 7 | |
5 | 3, 4 | le2or 168 | . . . . . 6 |
6 | 2, 5 | bltr 138 | . . . . 5 |
7 | lear 161 | . . . . 5 | |
8 | 6, 7 | le2or 168 | . . . 4 |
9 | oridm 110 | . . . 4 | |
10 | 8, 9 | lbtr 139 | . . 3 |
11 | 1, 10 | bltr 138 | . 2 |
12 | 11 | sklem 230 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 wt 8 wi3 14 |
This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-a3 32 ax-a4 33 ax-a5 34 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38 |
This theorem depends on definitions: df-a 40 df-t 41 df-f 42 df-i3 46 df-le1 130 df-le2 131 |
This theorem is referenced by: skmp3 245 mccune3 248 |
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