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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 4331 | . . . 4 | |
2 | frirrg 4323 | . . . 4 | |
3 | 1, 2 | syl3an1 1260 | . . 3 |
4 | 3 | 3expa 1192 | . 2 |
5 | df-3an 969 | . . 3 | |
6 | df-wetr 4307 | . . . . . . . . . 10 | |
7 | 6 | simprbi 273 | . . . . . . . . 9 |
8 | 7 | adantr 274 | . . . . . . . 8 |
9 | 8 | r19.21bi 2552 | . . . . . . 7 |
10 | 9 | r19.21bi 2552 | . . . . . 6 |
11 | 10 | anasss 397 | . . . . 5 |
12 | 11 | r19.21bi 2552 | . . . 4 |
13 | 12 | anasss 397 | . . 3 |
14 | 5, 13 | sylan2b 285 | . 2 |
15 | 4, 14 | ispod 4277 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 w3a 967 wcel 2135 wral 2442 class class class wbr 3977 wpo 4267 wfr 4301 wwe 4303 |
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 ax-sep 4095 |
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-ne 2335 df-ral 2447 df-v 2724 df-dif 3114 df-un 3116 df-in 3118 df-ss 3125 df-sn 3577 df-pr 3578 df-op 3580 df-br 3978 df-po 4269 df-frfor 4304 df-frind 4305 df-wetr 4307 |
This theorem is referenced by: (None) |
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