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Mirrors > Home > ILE Home > Th. List > nngt0d | Unicode version |
Description: A positive integer is positive. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
nnge1d.1 |
Ref | Expression |
---|---|
nngt0d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnge1d.1 | . 2 | |
2 | nngt0 8745 | . 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 clt 7800 cn 8720 |
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-1re 7714 ax-addrcl 7717 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 |
This theorem is referenced by: flqdiv 10094 modqmulnn 10115 modifeq2int 10159 modaddmodup 10160 modaddmodlo 10161 modsumfzodifsn 10169 addmodlteq 10171 facubnd 10491 resqrexlemdecn 10784 modfsummodlemstep 11226 divcnv 11266 cvgratnnlemabsle 11296 efcllemp 11364 ege2le3 11377 eftlub 11396 eflegeo 11408 eirraplem 11483 dvdslelemd 11541 dvdsmod 11560 mulmoddvds 11561 divalgmod 11624 bezoutlemnewy 11684 bezoutlemstep 11685 sqgcd 11717 eucalglt 11738 qredeu 11778 prmind2 11801 nprm 11804 sqrt2irraplemnn 11857 divdenle 11875 qnumgt0 11876 hashdvds 11897 crth 11900 phimullem 11901 |
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