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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 4341 | . 2 | |
2 | elong 4333 | . . 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 2128 word 4322 con0 4323 |
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-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-in 3108 df-ss 3115 df-uni 3773 df-tr 4063 df-iord 4326 df-on 4328 |
This theorem is referenced by: onelon 4344 ordsson 4451 ordpwsucss 4526 tfr1onlemsucfn 6287 tfr1onlemsucaccv 6288 tfr1onlembfn 6291 tfr1onlemubacc 6293 tfr1onlemaccex 6295 tfrcllemsucfn 6300 tfrcllemsucaccv 6301 tfrcllembfn 6304 tfrcllemubacc 6306 tfrcllemaccex 6308 tfrcl 6311 |
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