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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 8044 | . 2 | |
2 | 1 | sseli 2995 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1433 cc 6979 cn 8039 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-cnex 7067 ax-resscn 7068 ax-1re 7070 ax-addrcl 7073 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-in 2979 df-ss 2986 df-int 3637 df-inn 8040 |
This theorem is referenced by: nn1m1nn 8057 nn1suc 8058 nnaddcl 8059 nnmulcl 8060 nnsub 8077 nndiv 8079 nndivtr 8080 nnnn0addcl 8318 nn0nnaddcl 8319 elnnnn0 8331 nnnegz 8354 zaddcllempos 8388 zaddcllemneg 8390 nnaddm1cl 8412 elz2 8419 zdiv 8435 zdivadd 8436 zdivmul 8437 nneoor 8449 nneo 8450 divfnzn 8706 qmulz 8708 qaddcl 8720 qnegcl 8721 qmulcl 8722 qreccl 8727 nnledivrp 8837 nn0ledivnn 8838 fseq1m1p1 9112 ubmelm1fzo 9235 subfzo0 9251 flqdiv 9323 addmodidr 9375 modfzo0difsn 9397 nn0ennn 9425 expnegap0 9484 expm1t 9504 nnsqcl 9545 nnlesq 9578 facdiv 9665 facndiv 9666 faclbnd 9668 bcn1 9685 bcn2m1 9696 nndivides 10202 modmulconst 10227 dvdsflip 10251 nn0enne 10302 nno 10306 divalgmod 10327 ndvdsadd 10331 modgcd 10382 gcddiv 10408 gcdmultiple 10409 gcdmultiplez 10410 rpmulgcd 10415 rplpwr 10416 sqgcd 10418 lcmgcdlem 10459 qredeq 10478 qredeu 10479 divgcdcoprm0 10483 cncongrcoprm 10488 prmind2 10502 isprm6 10526 sqrt2irr 10541 oddpwdclemodd 10550 |
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