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Mirrors > Home > ILE Home > Th. List > nnge1d | Unicode version |
Description: A positive integer is one or greater. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
nnge1d.1 |
Ref | Expression |
---|---|
nnge1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnge1d.1 | . 2 | |
2 | nnge1 8871 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 class class class wbr 3976 c1 7745 cle 7925 cn 8848 |
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-1re 7838 ax-addrcl 7841 ax-0lt1 7850 ax-0id 7852 ax-rnegex 7853 ax-pre-ltirr 7856 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 |
This theorem is referenced by: exbtwnzlemstep 10173 addmodlteq 10323 bernneq3 10566 facwordi 10642 faclbnd 10643 faclbnd3 10645 facavg 10648 bcval5 10665 1elfz0hash 10708 seq3coll 10741 fsumcl2lem 11325 eftlub 11617 eflegeo 11628 eirraplem 11703 isprm5lem 12052 divdenle 12108 eulerthlemrprm 12140 eulerthlema 12141 nninfdclemlt 12329 logbgcd1irraplemexp 13433 |
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