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Mirrors > Home > ILE Home > Th. List > nn0ge0d | Unicode version |
Description: A nonnegative integer is greater than or equal to zero. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
nn0red.1 |
Ref | Expression |
---|---|
nn0ge0d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0red.1 | . 2 | |
2 | nn0ge0 9130 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 class class class wbr 3976 cc0 7744 cle 7925 cn0 9105 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-setind 4508 ax-cnex 7835 ax-resscn 7836 ax-1cn 7837 ax-1re 7838 ax-icn 7839 ax-addcl 7840 ax-addrcl 7841 ax-mulcl 7842 ax-i2m1 7849 ax-0lt1 7850 ax-0id 7852 ax-rnegex 7853 ax-pre-ltirr 7856 ax-pre-ltwlin 7857 ax-pre-lttrn 7858 ax-pre-ltadd 7860 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-br 3977 df-opab 4038 df-xp 4604 df-cnv 4606 df-iota 5147 df-fv 5190 df-ov 5839 df-pnf 7926 df-mnf 7927 df-xr 7928 df-ltxr 7929 df-le 7930 df-inn 8849 df-n0 9106 |
This theorem is referenced by: flqmulnn0 10224 zmodfz 10271 addmodid 10297 modifeq2int 10311 modaddmodlo 10313 modsumfzodifsn 10321 addmodlteq 10323 expnnval 10448 nn0le2msqd 10621 facwordi 10642 faclbnd 10643 faclbnd6 10646 facavg 10648 geolim2 11439 mertenslemi1 11462 eftabs 11583 efcllemp 11585 efaddlem 11601 eftlub 11617 oexpneg 11799 divalglemnn 11840 divalglemnqt 11842 divalglemeunn 11843 divalg2 11848 dfgcd2 11932 gcdmultiple 11938 gcdmultiplez 11939 dvdssqlem 11948 nn0seqcvgd 11952 mulgcddvds 12005 isprm5lem 12052 nn0sqrtelqelz 12117 nonsq 12118 phibndlem 12127 dfphi2 12131 modprm0 12165 pythagtriplem3 12178 pythagtriplem10 12180 pythagtriplem6 12181 pythagtriplem7 12182 pythagtriplem12 12186 pythagtriplem14 12188 pcge0 12223 pcprmpw2 12243 pcmptdvds 12254 fldivp1 12257 pcbc 12260 qexpz 12261 pockthlem 12265 pockthg 12266 ennnfoneleminc 12287 logbgcd1irraplemexp 13433 |
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