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Mirrors > Home > ILE Home > Th. List > po2nr | Unicode version |
Description: A partial order relation has no 2-cycle loops. (Contributed by NM, 27-Mar-1997.) |
Ref | Expression |
---|---|
po2nr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | poirr 4279 | . . 3 | |
2 | 1 | adantrr 471 | . 2 |
3 | potr 4280 | . . . . . 6 | |
4 | 3 | 3exp2 1214 | . . . . 5 |
5 | 4 | com34 83 | . . . 4 |
6 | 5 | pm2.43d 50 | . . 3 |
7 | 6 | imp32 255 | . 2 |
8 | 2, 7 | mtod 653 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wcel 2135 class class class wbr 3976 wpo 4266 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-v 2723 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-po 4268 |
This theorem is referenced by: po3nr 4282 so2nr 4293 tridc 6856 |
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