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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omelon 4530 |
. 2
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2 | 1 | oneli 4358 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-nul 4062 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-iinf 4510 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-nul 3369 df-pw 3517 df-sn 3538 df-pr 3539 df-uni 3745 df-int 3780 df-tr 4035 df-iord 4296 df-on 4298 df-suc 4301 df-iom 4513 |
This theorem is referenced by: nnoni 4532 nnord 4533 omsson 4534 nnsucpred 4538 nnpredcl 4544 frecrdg 6313 onasuc 6370 onmsuc 6377 nna0 6378 nnm0 6379 nnasuc 6380 nnmsuc 6381 nnsucelsuc 6395 nnsucsssuc 6396 nntri2or2 6402 nntr2 6407 nnaordi 6412 nnaword1 6417 nnaordex 6431 phpelm 6768 phplem4on 6769 omp1eomlem 6987 finnum 7056 pion 7142 prarloclemlo 7326 ennnfonelemk 11949 pwle2 13366 |
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