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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 2233 | . . . . 5 | |
2 | 1 | anbi2d 461 | . . . 4 |
3 | ordeq 4355 | . . . 4 | |
4 | 2, 3 | imbi12d 233 | . . 3 |
5 | dford3 4350 | . . . . . 6 | |
6 | 5 | simprbi 273 | . . . . 5 |
7 | 6 | r19.21bi 2558 | . . . 4 |
8 | ordelss 4362 | . . . 4 | |
9 | simpl 108 | . . . 4 | |
10 | trssord 4363 | . . . 4 | |
11 | 7, 8, 9, 10 | syl3anc 1233 | . . 3 |
12 | 4, 11 | vtoclg 2790 | . 2 |
13 | 12 | anabsi7 576 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 wral 2448 wss 3121 wtr 4085 word 4345 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-in 3127 df-ss 3134 df-uni 3795 df-tr 4086 df-iord 4349 |
This theorem is referenced by: tron 4365 ordelon 4366 ordsucg 4484 ordwe 4558 smores 6269 |
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