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Mirrors > Home > QLE Home > Th. List > wdwom | Unicode version |
Description: Prove 2-variable WOML rule in WDOL. This will make all WOML theorems available to us. The proof does not use ax-r3 439 or ax-wom 361. Since this is the same as ax-wom 361, from here on we will freely use those theorems invoking ax-wom 361. |
Ref | Expression |
---|---|
wdwom.1 |
Ref | Expression |
---|---|
wdwom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-i2 45 | . . 3 | |
2 | 1 | ax-r1 35 | . 2 |
3 | le1 146 | . . 3 | |
4 | df-i5 48 | . . . . . 6 | |
5 | df-i1 44 | . . . . . . . . 9 | |
6 | wdwom.1 | . . . . . . . . 9 | |
7 | 5, 6 | ax-r2 36 | . . . . . . . 8 |
8 | 7 | wql1lem 287 | . . . . . . 7 |
9 | or4 84 | . . . . . . . . . 10 | |
10 | anor1 88 | . . . . . . . . . . . . 13 | |
11 | 10 | ax-r1 35 | . . . . . . . . . . . 12 |
12 | 11 | lor 70 | . . . . . . . . . . 11 |
13 | 12 | ax-r5 38 | . . . . . . . . . 10 |
14 | 9, 13 | ax-r2 36 | . . . . . . . . 9 |
15 | or12 80 | . . . . . . . . 9 | |
16 | df-cmtr 134 | . . . . . . . . 9 | |
17 | 14, 15, 16 | 3tr1 63 | . . . . . . . 8 |
18 | wdcom 1103 | . . . . . . . 8 | |
19 | 17, 18 | ax-r2 36 | . . . . . . 7 |
20 | 8, 19 | skr0 242 | . . . . . 6 |
21 | 4, 20 | ax-r2 36 | . . . . 5 |
22 | 21 | ax-r1 35 | . . . 4 |
23 | i5lei2 348 | . . . 4 | |
24 | 22, 23 | bltr 138 | . . 3 |
25 | 3, 24 | lebi 145 | . 2 |
26 | 2, 25 | ax-r2 36 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 wt 8 wi1 12 wi2 13 wi5 16 wcmtr 29 |
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 ax-wdol 1102 |
This theorem depends on definitions: df-b 39 df-a 40 df-t 41 df-f 42 df-i1 44 df-i2 45 df-i5 48 df-le1 130 df-le2 131 df-cmtr 134 |
This theorem is referenced by: (None) |
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