Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 4308 | . . 3 | |
3 | 1, 2 | mpan 422 | . 2 |
4 | sotritric.tri | . . 3 | |
5 | 3orass 976 | . . . 4 | |
6 | ax-1 6 | . . . . 5 | |
7 | pm2.24 616 | . . . . 5 | |
8 | 6, 7 | jaoi 711 | . . . 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 703 w3o 972 wceq 1348 wcel 2141 class class class wbr 3989 wor 4280 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3or 974 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-un 3125 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-po 4281 df-iso 4282 |
This theorem is referenced by: nqtric 7361 |
Copyright terms: Public domain | W3C validator |