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Mirrors > Home > QLE Home > Th. List > oadistd | Unicode version |
Description: OA distributive law. |
Ref | Expression |
---|---|
oadistd.1 | |
oadistd.2 | |
oadistd.3 | |
oadistd.4 |
Ref | Expression |
---|---|
oadistd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oadistd.2 | . . . . . . . . . 10 | |
2 | oadistd.3 | . . . . . . . . . 10 | |
3 | 1, 2 | le2or 168 | . . . . . . . . 9 |
4 | oridm 110 | . . . . . . . . 9 | |
5 | 3, 4 | lbtr 139 | . . . . . . . 8 |
6 | 5 | lelan 167 | . . . . . . 7 |
7 | 6 | df2le2 136 | . . . . . 6 |
8 | 7 | ax-r1 35 | . . . . 5 |
9 | df-i0 43 | . . . . . . . 8 | |
10 | 9 | lan 77 | . . . . . . 7 |
11 | oadistd.1 | . . . . . . . 8 | |
12 | leo 158 | . . . . . . . . 9 | |
13 | 9 | ax-r1 35 | . . . . . . . . 9 |
14 | 12, 13 | lbtr 139 | . . . . . . . 8 |
15 | 11, 14 | oagen1b 1015 | . . . . . . 7 |
16 | 10, 15 | ax-r2 36 | . . . . . 6 |
17 | 16 | lan 77 | . . . . 5 |
18 | 8, 17 | ax-r2 36 | . . . 4 |
19 | lear 161 | . . . . 5 | |
20 | oadistd.4 | . . . . . . . . 9 | |
21 | 20 | df2le2 136 | . . . . . . . 8 |
22 | 21 | ax-r1 35 | . . . . . . 7 |
23 | an32 83 | . . . . . . 7 | |
24 | 22, 23 | ax-r2 36 | . . . . . 6 |
25 | lea 160 | . . . . . 6 | |
26 | 24, 25 | bltr 138 | . . . . 5 |
27 | 19, 26 | letr 137 | . . . 4 |
28 | 18, 27 | bltr 138 | . . 3 |
29 | leor 159 | . . 3 | |
30 | 28, 29 | letr 137 | . 2 |
31 | ledi 174 | . 2 | |
32 | 30, 31 | lebi 145 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wle 2 wn 4 wo 6 wa 7 wi0 11 wi2 13 |
This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-a3 32 ax-a5 34 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38 ax-3oa 998 |
This theorem depends on definitions: df-a 40 df-t 41 df-f 42 df-i0 43 df-i1 44 df-i2 45 df-le1 130 df-le2 131 |
This theorem is referenced by: (None) |
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