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Mirrors > Home > ILE Home > Th. List > po3nr | Unicode version |
Description: A partial order relation has no 3-cycle loops. (Contributed by NM, 27-Mar-1997.) |
Ref | Expression |
---|---|
po3nr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | po2nr 4046 | . . 3 | |
2 | 1 | 3adantr2 1064 | . 2 |
3 | df-3an 887 | . . 3 | |
4 | potr 4045 | . . . 4 | |
5 | 4 | anim1d 319 | . . 3 |
6 | 3, 5 | syl5bi 141 | . 2 |
7 | 2, 6 | mtod 589 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 w3a 885 wcel 1393 class class class wbr 3764 wpo 4031 |
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 |
This theorem is referenced by: so3nr 4059 |
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