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Mirrors > Home > ILE Home > Th. List > sotritric | Unicode version |
Description: A trichotomy relationship, given a trichotomous order. (Contributed by Jim Kingdon, 28-Sep-2019.) |
Ref | Expression |
---|---|
sotritric.or | |
sotritric.tri |
Ref | Expression |
---|---|
sotritric |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sotritric.or | . . 3 | |
2 | sotricim 4284 | . . 3 | |
3 | 1, 2 | mpan 421 | . 2 |
4 | sotritric.tri | . . 3 | |
5 | 3orass 966 | . . . 4 | |
6 | ax-1 6 | . . . . 5 | |
7 | pm2.24 611 | . . . . 5 | |
8 | 6, 7 | jaoi 706 | . . . 4 |
9 | 5, 8 | sylbi 120 | . . 3 |
10 | 4, 9 | syl 14 | . 2 |
11 | 3, 10 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 698 w3o 962 wceq 1335 wcel 2128 class class class wbr 3966 wor 4256 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-po 4257 df-iso 4258 |
This theorem is referenced by: nqtric 7320 |
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