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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 9002 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 class class class wbr 3929 cc0 7620 cle 7801 cn0 8977 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 ax-cnex 7711 ax-resscn 7712 ax-1cn 7713 ax-1re 7714 ax-icn 7715 ax-addcl 7716 ax-addrcl 7717 ax-mulcl 7718 ax-i2m1 7725 ax-0lt1 7726 ax-0id 7728 ax-rnegex 7729 ax-pre-ltirr 7732 ax-pre-ltwlin 7733 ax-pre-lttrn 7734 ax-pre-ltadd 7736 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-nel 2404 df-ral 2421 df-rex 2422 df-rab 2425 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-br 3930 df-opab 3990 df-xp 4545 df-cnv 4547 df-iota 5088 df-fv 5131 df-ov 5777 df-pnf 7802 df-mnf 7803 df-xr 7804 df-ltxr 7805 df-le 7806 df-inn 8721 df-n0 8978 |
This theorem is referenced by: flqmulnn0 10072 zmodfz 10119 addmodid 10145 modifeq2int 10159 modaddmodlo 10161 modsumfzodifsn 10169 addmodlteq 10171 expnnval 10296 nn0le2msqd 10465 facwordi 10486 faclbnd 10487 faclbnd6 10490 facavg 10492 geolim2 11281 mertenslemi1 11304 eftabs 11362 efcllemp 11364 efaddlem 11380 eftlub 11396 oexpneg 11574 divalglemnn 11615 divalglemnqt 11617 divalglemeunn 11618 divalg2 11623 dfgcd2 11702 gcdmultiple 11708 gcdmultiplez 11709 dvdssqlem 11718 nn0seqcvgd 11722 mulgcddvds 11775 nn0sqrtelqelz 11884 nonsq 11885 phibndlem 11892 dfphi2 11896 ennnfoneleminc 11924 |
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