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Mirrors > Home > ILE Home > Th. List > sotricim | Unicode version |
Description: One direction of sotritric 4241 holds for all weakly linear orders. (Contributed by Jim Kingdon, 28-Sep-2019.) |
Ref | Expression |
---|---|
sotricim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sonr 4234 | . . . . . . 7 | |
2 | 1 | adantrr 470 | . . . . . 6 |
3 | 2 | 3adant3 1001 | . . . . 5 |
4 | breq2 3928 | . . . . . . 7 | |
5 | 4 | biimprcd 159 | . . . . . 6 |
6 | 5 | 3ad2ant3 1004 | . . . . 5 |
7 | 3, 6 | mtod 652 | . . . 4 |
8 | 7 | 3expia 1183 | . . 3 |
9 | so2nr 4238 | . . . 4 | |
10 | imnan 679 | . . . 4 | |
11 | 9, 10 | sylibr 133 | . . 3 |
12 | 8, 11 | jcad 305 | . 2 |
13 | ioran 741 | . 2 | |
14 | 12, 13 | syl6ibr 161 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 697 w3a 962 wceq 1331 wcel 1480 class class class wbr 3924 wor 4212 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-po 4213 df-iso 4214 |
This theorem is referenced by: sotritric 4241 |
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