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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 965 | . . 3 | |
2 | df-wetr 4294 | . . . . . . . . 9 | |
3 | 2 | simprbi 273 | . . . . . . . 8 |
4 | 3 | r19.21bi 2545 | . . . . . . 7 |
5 | 4 | r19.21bi 2545 | . . . . . 6 |
6 | 5 | anasss 397 | . . . . 5 |
7 | 6 | r19.21bi 2545 | . . . 4 |
8 | 7 | anasss 397 | . . 3 |
9 | 1, 8 | sylan2b 285 | . 2 |
10 | epel 4252 | . . 3 | |
11 | epel 4252 | . . 3 | |
12 | 10, 11 | anbi12i 456 | . 2 |
13 | epel 4252 | . 2 | |
14 | 9, 12, 13 | 3imtr3g 203 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 963 wcel 2128 wral 2435 class class class wbr 3965 cep 4247 wfr 4288 wwe 4290 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-eprel 4249 df-wetr 4294 |
This theorem is referenced by: wessep 4537 |
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