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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 4630 |
. 2
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2 | eloni 4396 |
. 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-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 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-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4139 ax-nul 4147 ax-pow 4195 ax-pr 4230 ax-un 4454 ax-iinf 4608 |
This theorem depends on definitions: df-bi 117 df-3an 982 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-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3595 df-sn 3616 df-pr 3617 df-uni 3828 df-int 3863 df-tr 4120 df-iord 4387 df-on 4389 df-suc 4392 df-iom 4611 |
This theorem is referenced by: nnsucsssuc 6521 nnsucuniel 6524 nntri1 6525 nnsseleq 6530 nntr2 6532 phplem1 6884 phplem2 6885 phplem3 6886 phplem4 6887 phplem4dom 6894 nndomo 6896 dif1en 6911 nnwetri 6948 unsnfi 6951 ctmlemr 7141 nnnninf 7159 nnnninfeq 7161 nnnninfeq2 7162 nninfisol 7166 piord 7345 addnidpig 7370 archnqq 7451 frecfzennn 10463 hashp1i 10831 ennnfonelemk 12462 ennnfonelemg 12465 ennnfonelemhf1o 12475 ennnfonelemhom 12477 ctinfom 12490 nnsf 15241 peano4nninf 15242 nninfsellemeq 15250 |
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