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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 4394 |
. 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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-in 3150 df-ss 3157 df-uni 3828 df-tr 4120 df-iord 4387 df-on 4389 |
This theorem is referenced by: elon2 4397 onelon 4405 onin 4407 onelss 4408 ontr1 4410 onordi 4447 onss 4513 onsuc 4521 onsucb 4523 onsucmin 4527 onsucelsucr 4528 onintonm 4537 ordsucunielexmid 4551 onsucuni2 4584 nnord 4632 tfrlem1 6337 tfrlemisucaccv 6354 tfrlemibfn 6357 tfrlemiubacc 6359 tfrexlem 6363 tfr1onlemsucfn 6369 tfr1onlemsucaccv 6370 tfr1onlembfn 6373 tfr1onlemubacc 6375 tfrcllemsucfn 6382 tfrcllemsucaccv 6383 tfrcllembfn 6386 tfrcllemubacc 6388 sucinc2 6475 phplem4on 6899 ordiso 7069 |
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