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Mirrors > Home > QLE Home > Th. List > d4oa | Unicode version |
Description: Variant of proper 4-OA proved from OA distributive law. |
Ref | Expression |
---|---|
d4oa.2 | |
d4oa.1 |
Ref | Expression |
---|---|
d4oa |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-a2 31 | . . . 4 | |
2 | 1 | lan 77 | . . 3 |
3 | id 59 | . . . 4 | |
4 | d4oa.2 | . . . . 5 | |
5 | d4oa.1 | . . . . 5 | |
6 | 4, 5 | 2or 72 | . . . 4 |
7 | leid 148 | . . . 4 | |
8 | leor 159 | . . . 4 | |
9 | leo 158 | . . . 4 | |
10 | leor 159 | . . . . 5 | |
11 | 4 | ax-r1 35 | . . . . 5 |
12 | 10, 11 | lbtr 139 | . . . 4 |
13 | 3, 6, 7, 8, 9, 12 | ax-oadist 994 | . . 3 |
14 | 2, 13 | ax-r2 36 | . 2 |
15 | 5 | lan 77 | . . . . . 6 |
16 | anass 76 | . . . . . . 7 | |
17 | 16 | ax-r1 35 | . . . . . 6 |
18 | 15, 17 | ax-r2 36 | . . . . 5 |
19 | id 59 | . . . . . . 7 | |
20 | 19 | d3oa 995 | . . . . . 6 |
21 | 20 | leran 153 | . . . . 5 |
22 | 18, 21 | bltr 138 | . . . 4 |
23 | ancom 74 | . . . . . 6 | |
24 | ancom 74 | . . . . . 6 | |
25 | 23, 24 | 2or 72 | . . . . 5 |
26 | 25 | d3oa 995 | . . . 4 |
27 | 22, 26 | letr 137 | . . 3 |
28 | 4 | d3oa 995 | . . 3 |
29 | 27, 28 | lel2or 170 | . 2 |
30 | 14, 29 | bltr 138 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wle 2 wo 6 wa 7 wi1 12 |
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-r3 439 ax-oadist 994 |
This theorem depends on definitions: df-b 39 df-a 40 df-t 41 df-f 42 df-i0 43 df-i1 44 df-i2 45 df-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: d6oa 997 |
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