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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 4095 | . . . 4 | |
2 | frirrg 4087 | . . . 4 | |
3 | 1, 2 | syl3an1 1168 | . . 3 |
4 | 3 | 3expa 1104 | . 2 |
5 | df-3an 887 | . . 3 | |
6 | df-wetr 4071 | . . . . . . . . . 10 | |
7 | 6 | simprbi 260 | . . . . . . . . 9 |
8 | 7 | adantr 261 | . . . . . . . 8 |
9 | 8 | r19.21bi 2407 | . . . . . . 7 |
10 | 9 | r19.21bi 2407 | . . . . . 6 |
11 | 10 | anasss 379 | . . . . 5 |
12 | 11 | r19.21bi 2407 | . . . 4 |
13 | 12 | anasss 379 | . . 3 |
14 | 5, 13 | sylan2b 271 | . 2 |
15 | 4, 14 | ispod 4041 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 w3a 885 wcel 1393 wral 2306 class class class wbr 3764 wpo 4031 wfr 4065 wwe 4067 |
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 ax-sep 3875 |
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-ne 2206 df-ral 2311 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-po 4033 df-frfor 4068 df-frind 4069 df-wetr 4071 |
This theorem is referenced by: (None) |
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