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Mirrors > Home > ILE Home > Th. List > wetrep | Unicode version |
Description: An epsilon well-ordering is a transitive relation. (Contributed by NM, 22-Apr-1994.) |
Ref | Expression |
---|---|
wetrep |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 949 | . . 3 | |
2 | df-wetr 4226 | . . . . . . . . 9 | |
3 | 2 | simprbi 273 | . . . . . . . 8 |
4 | 3 | r19.21bi 2497 | . . . . . . 7 |
5 | 4 | r19.21bi 2497 | . . . . . 6 |
6 | 5 | anasss 396 | . . . . 5 |
7 | 6 | r19.21bi 2497 | . . . 4 |
8 | 7 | anasss 396 | . . 3 |
9 | 1, 8 | sylan2b 285 | . 2 |
10 | epel 4184 | . . 3 | |
11 | epel 4184 | . . 3 | |
12 | 10, 11 | anbi12i 455 | . 2 |
13 | epel 4184 | . 2 | |
14 | 9, 12, 13 | 3imtr3g 203 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 947 wcel 1465 wral 2393 class class class wbr 3899 cep 4179 wfr 4220 wwe 4222 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-eprel 4181 df-wetr 4226 |
This theorem is referenced by: wessep 4462 |
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