Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 4062 | . . 3 | |
2 | 1 | adantrr 462 | . 2 |
3 | potr 4063 | . . . . . 6 | |
4 | 3 | 3exp2 1156 | . . . . 5 |
5 | 4 | com34 82 | . . . 4 |
6 | 5 | pm2.43d 49 | . . 3 |
7 | 6 | imp32 253 | . 2 |
8 | 2, 7 | mtod 621 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wcel 1433 class class class wbr 3785 wpo 4049 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-po 4051 |
This theorem is referenced by: po3nr 4065 so2nr 4076 |
Copyright terms: Public domain | W3C validator |