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Mirrors > Home > QLE Home > Th. List > sklem | Unicode version |
Description: Soundness lemma. |
Ref | Expression |
---|---|
sklem.1 |
Ref | Expression |
---|---|
sklem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | or12 80 | . . 3 | |
2 | df-t 41 | . . . . . 6 | |
3 | 2 | ax-r5 38 | . . . . 5 |
4 | 3 | ax-r1 35 | . . . 4 |
5 | ax-a3 32 | . . . 4 | |
6 | ax-a2 31 | . . . 4 | |
7 | 4, 5, 6 | 3tr2 64 | . . 3 |
8 | 1, 7 | ax-r2 36 | . 2 |
9 | sklem.1 | . . . 4 | |
10 | 9 | df-le2 131 | . . 3 |
11 | 10 | lor 70 | . 2 |
12 | or1 104 | . 2 | |
13 | 8, 11, 12 | 3tr2 64 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wle 2 wn 4 wo 6 wt 8 |
This theorem was proved from axioms: ax-a2 31 ax-a3 32 ax-a4 33 ax-r1 35 ax-r2 36 ax-r5 38 |
This theorem depends on definitions: df-t 41 df-le2 131 |
This theorem is referenced by: ska13 241 ska15 244 lei3 246 oaidlem1 294 id5id0 352 u1lemle1 710 u2lemle1 711 u3lemle1 712 u4lemle1 713 u5lemle1 714 lem3.3.3 1052 lem3.3.7i4e1 1069 lem3.3.7i4e2 1070 lem4.6.7 1101 |
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