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Mirrors > Home > ILE Home > Th. List > sotricim | Unicode version |
Description: One direction of sotritric 4061 holds for all weakly linear orders. (Contributed by Jim Kingdon, 28-Sep-2019.) |
Ref | Expression |
---|---|
sotricim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sonr 4054 | . . . . . . 7 | |
2 | 1 | adantrr 448 | . . . . . 6 |
3 | 2 | 3adant3 924 | . . . . 5 |
4 | breq2 3768 | . . . . . . 7 | |
5 | 4 | biimprcd 149 | . . . . . 6 |
6 | 5 | 3ad2ant3 927 | . . . . 5 |
7 | 3, 6 | mtod 589 | . . . 4 |
8 | 7 | 3expia 1106 | . . 3 |
9 | so2nr 4058 | . . . 4 | |
10 | imnan 624 | . . . 4 | |
11 | 9, 10 | sylibr 137 | . . 3 |
12 | 8, 11 | jcad 291 | . 2 |
13 | ioran 669 | . 2 | |
14 | 12, 13 | syl6ibr 151 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wo 629 w3a 885 wceq 1243 wcel 1393 class class class wbr 3764 wor 4032 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-po 4033 df-iso 4034 |
This theorem is referenced by: sotritric 4061 |
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