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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 8693 | . 2 | |
2 | 1 | sseli 3063 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 cc 7586 cn 8688 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-cnex 7679 ax-resscn 7680 ax-1re 7682 ax-addrcl 7685 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 df-in 3047 df-ss 3054 df-int 3742 df-inn 8689 |
This theorem is referenced by: nn1m1nn 8706 nn1suc 8707 nnaddcl 8708 nnmulcl 8709 nnsub 8727 nndiv 8729 nndivtr 8730 nnnn0addcl 8975 nn0nnaddcl 8976 elnnnn0 8988 nnnegz 9025 zaddcllempos 9059 zaddcllemneg 9061 nnaddm1cl 9083 elz2 9090 zdiv 9107 zdivadd 9108 zdivmul 9109 nneoor 9121 nneo 9122 divfnzn 9381 qmulz 9383 qaddcl 9395 qnegcl 9396 qmulcl 9397 qreccl 9402 nnledivrp 9521 nn0ledivnn 9522 fseq1m1p1 9843 nnsplit 9882 ubmelm1fzo 9971 subfzo0 9987 flqdiv 10062 addmodidr 10114 modfzo0difsn 10136 nn0ennn 10174 expnegap0 10269 expm1t 10289 nnsqcl 10330 nnlesq 10364 facdiv 10452 facndiv 10453 faclbnd 10455 bcn1 10472 bcn2m1 10483 arisum 11235 arisum2 11236 expcnvap0 11239 mertenslem2 11273 ef0lem 11293 efexp 11315 nndivides 11427 modmulconst 11452 dvdsflip 11476 nn0enne 11526 nno 11530 divalgmod 11551 ndvdsadd 11555 modgcd 11606 gcddiv 11634 gcdmultiple 11635 gcdmultiplez 11636 rpmulgcd 11641 rplpwr 11642 sqgcd 11644 lcmgcdlem 11685 qredeq 11704 qredeu 11705 divgcdcoprm0 11709 cncongrcoprm 11714 prmind2 11728 isprm6 11752 sqrt2irr 11767 oddpwdclemodd 11777 divnumden 11801 divdenle 11802 nn0gcdsq 11805 hashgcdlem 11830 dvexp 12771 |
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