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Mirrors > Home > MPE Home > Th. List > nnord | Structured version Visualization version Unicode version |
Description: A natural number is ordinal. (Contributed by NM, 17-Oct-1995.) |
Ref | Expression |
---|---|
nnord |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnon 7071 | . 2 | |
2 | eloni 5733 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 word 5722 con0 5723 com 7065 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-tr 4753 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 df-om 7066 |
This theorem is referenced by: nnlim 7078 nnsuc 7082 nnaordi 7698 nnaord 7699 nnaword 7707 nnmord 7712 nnmwordi 7715 nnawordex 7717 omsmo 7734 phplem1 8139 phplem2 8140 phplem3 8141 phplem4 8142 php 8144 php4 8147 nndomo 8154 ominf 8172 isinf 8173 pssnn 8178 dif1en 8193 unblem1 8212 isfinite2 8218 unfilem1 8224 inf3lem5 8529 inf3lem6 8530 cantnfp1lem2 8576 cantnfp1lem3 8577 dif1card 8833 pwsdompw 9026 ackbij1lem5 9046 ackbij1lem14 9055 ackbij1lem16 9057 ackbij1b 9061 ackbij2 9065 sornom 9099 infpssrlem4 9128 infpssrlem5 9129 fin23lem26 9147 fin23lem23 9148 isf32lem2 9176 isf32lem3 9177 isf32lem4 9178 domtriomlem 9264 axdc3lem2 9273 axdc3lem4 9275 canthp1lem2 9475 elni2 9699 piord 9702 addnidpi 9723 indpi 9729 om2uzf1oi 12752 fzennn 12767 hashp1i 13191 bnj529 30811 bnj1098 30854 bnj570 30975 bnj594 30982 bnj580 30983 bnj967 31015 bnj1001 31028 bnj1053 31044 bnj1071 31045 hfun 32285 finminlem 32312 finxpsuclem 33234 finxpsuc 33235 wepwso 37613 |
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