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Mirrors > Home > ILE Home > Th. List > nnord | Unicode version |
Description: A natural number is ordinal. (Contributed by NM, 17-Oct-1995.) |
Ref | Expression |
---|---|
nnord |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnon 4461 |
. 2
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2 | eloni 4235 |
. 2
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3 | 1, 2 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-13 1459 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-nul 3994 ax-pow 4038 ax-pr 4069 ax-un 4293 ax-iinf 4440 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 df-nul 3311 df-pw 3459 df-sn 3480 df-pr 3481 df-uni 3684 df-int 3719 df-tr 3967 df-iord 4226 df-on 4228 df-suc 4231 df-iom 4443 |
This theorem is referenced by: nnsucsssuc 6318 nnsucuniel 6321 nntri1 6322 nnsseleq 6327 nntr2 6329 phplem1 6675 phplem2 6676 phplem3 6677 phplem4 6678 phplem4dom 6685 nndomo 6687 dif1en 6702 nnwetri 6733 unsnfi 6736 ctmlemr 6908 nnnninf 6935 piord 7020 addnidpig 7045 archnqq 7126 frecfzennn 10040 hashp1i 10397 ennnfonelemk 11705 ennnfonelemg 11708 ennnfonelemhf1o 11718 ennnfonelemhom 11720 ctinfom 11733 nnsf 12783 peano4nninf 12784 nninfalllemn 12786 nninfsellemeq 12794 |
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