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Mirrors > Home > ILE Home > Th. List > wepo | Unicode version |
Description: A well-ordering is a partial ordering. (Contributed by Jim Kingdon, 23-Sep-2021.) |
Ref | Expression |
---|---|
wepo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wefr 4280 | . . . 4 | |
2 | frirrg 4272 | . . . 4 | |
3 | 1, 2 | syl3an1 1249 | . . 3 |
4 | 3 | 3expa 1181 | . 2 |
5 | df-3an 964 | . . 3 | |
6 | df-wetr 4256 | . . . . . . . . . 10 | |
7 | 6 | simprbi 273 | . . . . . . . . 9 |
8 | 7 | adantr 274 | . . . . . . . 8 |
9 | 8 | r19.21bi 2520 | . . . . . . 7 |
10 | 9 | r19.21bi 2520 | . . . . . 6 |
11 | 10 | anasss 396 | . . . . 5 |
12 | 11 | r19.21bi 2520 | . . . 4 |
13 | 12 | anasss 396 | . . 3 |
14 | 5, 13 | sylan2b 285 | . 2 |
15 | 4, 14 | ispod 4226 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 w3a 962 wcel 1480 wral 2416 class class class wbr 3929 wpo 4216 wfr 4250 wwe 4252 |
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 2121 ax-sep 4046 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-po 4218 df-frfor 4253 df-frind 4254 df-wetr 4256 |
This theorem is referenced by: (None) |
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