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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elong 4373 |
. 2
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2 | 1 | ibi 176 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-in 3135 df-ss 3142 df-uni 3810 df-tr 4102 df-iord 4366 df-on 4368 |
This theorem is referenced by: elon2 4376 onelon 4384 onin 4386 onelss 4387 ontr1 4389 onordi 4426 onss 4492 onsuc 4500 onsucb 4502 onsucmin 4506 onsucelsucr 4507 onintonm 4516 ordsucunielexmid 4530 onsucuni2 4563 nnord 4611 tfrlem1 6308 tfrlemisucaccv 6325 tfrlemibfn 6328 tfrlemiubacc 6330 tfrexlem 6334 tfr1onlemsucfn 6340 tfr1onlemsucaccv 6341 tfr1onlembfn 6344 tfr1onlemubacc 6346 tfrcllemsucfn 6353 tfrcllemsucaccv 6354 tfrcllembfn 6357 tfrcllemubacc 6359 sucinc2 6446 phplem4on 6866 ordiso 7034 |
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