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Mirrors > Home > ILE Home > Th. List > so2nr | Unicode version |
Description: A strict order relation has no 2-cycle loops. (Contributed by NM, 21-Jan-1996.) |
Ref | Expression |
---|---|
so2nr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sopo 4243 | . 2 | |
2 | po2nr 4239 | . 2 | |
3 | 1, 2 | sylan 281 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wcel 1481 class class class wbr 3937 wpo 4224 wor 4225 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-po 4226 df-iso 4227 |
This theorem is referenced by: sotricim 4253 cauappcvgprlemdisj 7483 cauappcvgprlemladdru 7488 cauappcvgprlemladdrl 7489 caucvgprlemnbj 7499 caucvgprprlemnbj 7525 suplocexprlemmu 7550 ltnsym2 7878 |
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