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Mirrors > Home > QLE Home > Th. List > oa3-5lem | Unicode version |
Description: Lemma for 3-OA(5). Equivalence with substitution into 6-OA dual. |
Ref | Expression |
---|---|
oa3-5lem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | or12 80 | . . . . . . 7 | |
2 | oridm 110 | . . . . . . . 8 | |
3 | 2 | lor 70 | . . . . . . 7 |
4 | 1, 3 | ax-r2 36 | . . . . . 6 |
5 | an1 106 | . . . . . . . 8 | |
6 | df-i1 44 | . . . . . . . 8 | |
7 | 5, 6 | ax-r2 36 | . . . . . . 7 |
8 | 7 | lor 70 | . . . . . 6 |
9 | 4, 8, 6 | 3tr1 63 | . . . . 5 |
10 | or12 80 | . . . . . . . . 9 | |
11 | ancom 74 | . . . . . . . . . . . 12 | |
12 | 11 | ax-r5 38 | . . . . . . . . . . 11 |
13 | oridm 110 | . . . . . . . . . . 11 | |
14 | 12, 13 | ax-r2 36 | . . . . . . . . . 10 |
15 | 14 | lor 70 | . . . . . . . . 9 |
16 | 10, 15 | ax-r2 36 | . . . . . . . 8 |
17 | ancom 74 | . . . . . . . . . 10 | |
18 | an1 106 | . . . . . . . . . 10 | |
19 | df-i1 44 | . . . . . . . . . 10 | |
20 | 17, 18, 19 | 3tr 65 | . . . . . . . . 9 |
21 | 20 | lor 70 | . . . . . . . 8 |
22 | 16, 21, 19 | 3tr1 63 | . . . . . . 7 |
23 | 22 | lan 77 | . . . . . 6 |
24 | ancom 74 | . . . . . 6 | |
25 | 23, 24 | ax-r2 36 | . . . . 5 |
26 | 9, 25 | 2or 72 | . . . 4 |
27 | 26 | lan 77 | . . 3 |
28 | 27 | lor 70 | . 2 |
29 | 28 | lan 77 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 wt 8 wi1 12 |
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 |
This theorem depends on definitions: df-a 40 df-t 41 df-f 42 df-i1 44 |
This theorem is referenced by: (None) |
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