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Mirrors > Home > ILE Home > Th. List > nnon | Unicode version |
Description: A natural number is an ordinal number. (Contributed by NM, 27-Jun-1994.) |
Ref | Expression |
---|---|
nnon |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omelon 4571 | . 2 | |
2 | 1 | oneli 4391 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2128 con0 4326 com 4552 |
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-in1 604 ax-in2 605 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-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4085 ax-nul 4093 ax-pow 4138 ax-pr 4172 ax-un 4396 ax-iinf 4550 |
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-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3396 df-pw 3546 df-sn 3567 df-pr 3568 df-uni 3775 df-int 3810 df-tr 4066 df-iord 4329 df-on 4331 df-suc 4334 df-iom 4553 |
This theorem is referenced by: nnoni 4573 nnord 4574 omsson 4575 nnsucpred 4579 nnpredcl 4585 frecrdg 6358 onasuc 6416 onmsuc 6423 nna0 6424 nnm0 6425 nnasuc 6426 nnmsuc 6427 nnsucelsuc 6441 nnsucsssuc 6442 nntri2or2 6448 nntr2 6453 nnaordi 6458 nnaword1 6463 nnaordex 6477 phpelm 6814 phplem4on 6815 omp1eomlem 7041 finnum 7121 pion 7233 prarloclemlo 7417 ennnfonelemk 12225 pwle2 13667 |
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