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Mirrors > Home > ILE Home > Th. List > ordelord | Unicode version |
Description: An element of an ordinal class is ordinal. Proposition 7.6 of [TakeutiZaring] p. 36. (Contributed by NM, 23-Apr-1994.) |
Ref | Expression |
---|---|
ordelord |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2141 | . . . . 5 | |
2 | 1 | anbi2d 451 | . . . 4 |
3 | ordeq 4127 | . . . 4 | |
4 | 2, 3 | imbi12d 232 | . . 3 |
5 | dford3 4122 | . . . . . 6 | |
6 | 5 | simprbi 269 | . . . . 5 |
7 | 6 | r19.21bi 2449 | . . . 4 |
8 | ordelss 4134 | . . . 4 | |
9 | simpl 107 | . . . 4 | |
10 | trssord 4135 | . . . 4 | |
11 | 7, 8, 9, 10 | syl3anc 1169 | . . 3 |
12 | 4, 11 | vtoclg 2658 | . 2 |
13 | 12 | anabsi7 545 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wcel 1433 wral 2348 wss 2973 wtr 3875 word 4117 |
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-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-in 2979 df-ss 2986 df-uni 3602 df-tr 3876 df-iord 4121 |
This theorem is referenced by: tron 4137 ordelon 4138 ordsucg 4246 ordwe 4318 smores 5930 |
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