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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 921 | . . 3 | |
2 | df-wetr 4089 | . . . . . . . . 9 | |
3 | 2 | simprbi 269 | . . . . . . . 8 |
4 | 3 | r19.21bi 2449 | . . . . . . 7 |
5 | 4 | r19.21bi 2449 | . . . . . 6 |
6 | 5 | anasss 391 | . . . . 5 |
7 | 6 | r19.21bi 2449 | . . . 4 |
8 | 7 | anasss 391 | . . 3 |
9 | 1, 8 | sylan2b 281 | . 2 |
10 | epel 4047 | . . 3 | |
11 | epel 4047 | . . 3 | |
12 | 10, 11 | anbi12i 447 | . 2 |
13 | epel 4047 | . 2 | |
14 | 9, 12, 13 | 3imtr3g 202 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 w3a 919 wcel 1433 wral 2348 class class class wbr 3785 cep 4042 wfr 4083 wwe 4085 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-eprel 4044 df-wetr 4089 |
This theorem is referenced by: wessep 4320 |
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