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Mirrors > Home > ILE Home > Th. List > nncn | Unicode version |
Description: A positive integer is a complex number. (Contributed by NM, 18-Aug-1999.) |
Ref | Expression |
---|---|
nncn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnsscn 8718 | . 2 | |
2 | 1 | sseli 3088 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 cc 7611 cn 8713 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-cnex 7704 ax-resscn 7705 ax-1re 7707 ax-addrcl 7710 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-in 3072 df-ss 3079 df-int 3767 df-inn 8714 |
This theorem is referenced by: nn1m1nn 8731 nn1suc 8732 nnaddcl 8733 nnmulcl 8734 nnsub 8752 nndiv 8754 nndivtr 8755 nnnn0addcl 9000 nn0nnaddcl 9001 elnnnn0 9013 nnnegz 9050 zaddcllempos 9084 zaddcllemneg 9086 nnaddm1cl 9108 elz2 9115 zdiv 9132 zdivadd 9133 zdivmul 9134 nneoor 9146 nneo 9147 divfnzn 9406 qmulz 9408 qaddcl 9420 qnegcl 9421 qmulcl 9422 qreccl 9427 nnledivrp 9546 nn0ledivnn 9547 fseq1m1p1 9868 nnsplit 9907 ubmelm1fzo 9996 subfzo0 10012 flqdiv 10087 addmodidr 10139 modfzo0difsn 10161 nn0ennn 10199 expnegap0 10294 expm1t 10314 nnsqcl 10355 nnlesq 10389 facdiv 10477 facndiv 10478 faclbnd 10480 bcn1 10497 bcn2m1 10508 arisum 11260 arisum2 11261 expcnvap0 11264 mertenslem2 11298 ef0lem 11355 efexp 11377 nndivides 11489 modmulconst 11514 dvdsflip 11538 nn0enne 11588 nno 11592 divalgmod 11613 ndvdsadd 11617 modgcd 11668 gcddiv 11696 gcdmultiple 11697 gcdmultiplez 11698 rpmulgcd 11703 rplpwr 11704 sqgcd 11706 lcmgcdlem 11747 qredeq 11766 qredeu 11767 divgcdcoprm0 11771 cncongrcoprm 11776 prmind2 11790 isprm6 11814 sqrt2irr 11829 oddpwdclemodd 11839 divnumden 11863 divdenle 11864 nn0gcdsq 11867 hashgcdlem 11892 dvexp 12833 |
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