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Mirrors > Home > ILE Home > Th. List > ordelon | Unicode version |
Description: An element of an ordinal class is an ordinal number. (Contributed by NM, 26-Oct-2003.) |
Ref | Expression |
---|---|
ordelon |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordelord 4366 | . 2 | |
2 | elong 4358 | . . 3 | |
3 | 2 | adantl 275 | . 2 |
4 | 1, 3 | mpbird 166 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 2141 word 4347 con0 4348 |
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 3797 df-tr 4088 df-iord 4351 df-on 4353 |
This theorem is referenced by: onelon 4369 ordsson 4476 ordpwsucss 4551 tfr1onlemsucfn 6319 tfr1onlemsucaccv 6320 tfr1onlembfn 6323 tfr1onlemubacc 6325 tfr1onlemaccex 6327 tfrcllemsucfn 6332 tfrcllemsucaccv 6333 tfrcllembfn 6336 tfrcllemubacc 6338 tfrcllemaccex 6340 tfrcl 6343 |
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