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Mirrors > Home > ILE Home > Th. List > nnnn0 | Unicode version |
Description: A positive integer is a nonnegative integer. (Contributed by NM, 9-May-2004.) |
Ref | Expression |
---|---|
nnnn0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnssnn0 9004 |
. 2
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2 | 1 | sseli 3098 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-n0 9002 |
This theorem is referenced by: nnnn0i 9009 elnnnn0b 9045 elnnnn0c 9046 elnn0z 9091 elz2 9146 nn0ind-raph 9192 zindd 9193 fzo1fzo0n0 9991 ubmelfzo 10008 elfzom1elp1fzo 10010 fzo0sn0fzo1 10029 modqmulnn 10146 expnegap0 10332 expcllem 10335 expcl2lemap 10336 expap0 10354 expeq0 10355 mulexpzap 10364 expnlbnd 10447 apexp1 10496 facdiv 10516 faclbnd 10519 faclbnd3 10521 faclbnd6 10522 resqrexlemlo 10817 absexpzap 10884 nnf1o 11177 summodclem2a 11182 fsum3 11188 arisum 11299 expcnvap0 11303 expcnv 11305 geo2sum 11315 geo2lim 11317 geoisum1c 11321 0.999... 11322 mertenslem2 11337 fprodseq 11384 ef0lem 11403 ege2le3 11414 efaddlem 11417 efexp 11425 nn0enne 11635 nnehalf 11637 nno 11639 nn0o 11640 divalg2 11659 ndvdssub 11663 gcddiv 11743 gcdmultiple 11744 gcdmultiplez 11745 rpmulgcd 11750 rplpwr 11751 dvdssqlem 11754 eucalgf 11772 1nprm 11831 isprm6 11861 prmdvdsexp 11862 pw2dvds 11880 oddpwdc 11888 phicl2 11926 phibndlem 11928 phiprmpw 11934 crth 11936 hashgcdlem 11939 ennnfonelemjn 11951 dvexp 12883 logbgcd1irr 13092 |
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