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Mirrors > Home > ILE Home > Th. List > eloni | Unicode version |
Description: An ordinal number has the ordinal property. (Contributed by NM, 5-Jun-1994.) |
Ref | Expression |
---|---|
eloni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elong 4290 | . 2 | |
2 | 1 | ibi 175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 word 4279 con0 4280 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-in 3072 df-ss 3079 df-uni 3732 df-tr 4022 df-iord 4283 df-on 4285 |
This theorem is referenced by: elon2 4293 onelon 4301 onin 4303 onelss 4304 ontr1 4306 onordi 4343 onss 4404 suceloni 4412 sucelon 4414 onsucmin 4418 onsucelsucr 4419 onintonm 4428 ordsucunielexmid 4441 onsucuni2 4474 nnord 4520 tfrlem1 6198 tfrlemisucaccv 6215 tfrlemibfn 6218 tfrlemiubacc 6220 tfrexlem 6224 tfr1onlemsucfn 6230 tfr1onlemsucaccv 6231 tfr1onlembfn 6234 tfr1onlemubacc 6236 tfrcllemsucfn 6243 tfrcllemsucaccv 6244 tfrcllembfn 6247 tfrcllemubacc 6249 sucinc2 6335 phplem4on 6754 ordiso 6914 |
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