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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 8853 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2128 class class class wbr 3965 cc0 7727 clt 7907 cn 8828 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-un 4393 ax-setind 4495 ax-cnex 7818 ax-resscn 7819 ax-1re 7821 ax-addrcl 7824 ax-0lt1 7833 ax-0id 7835 ax-rnegex 7836 ax-pre-ltirr 7839 ax-pre-ltwlin 7840 ax-pre-lttrn 7841 ax-pre-ltadd 7843 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-nel 2423 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-int 3808 df-br 3966 df-opab 4026 df-xp 4591 df-cnv 4593 df-iota 5134 df-fv 5177 df-ov 5824 df-pnf 7909 df-mnf 7910 df-xr 7911 df-ltxr 7912 df-le 7913 df-inn 8829 |
This theorem is referenced by: flqdiv 10215 modqmulnn 10236 modifeq2int 10280 modaddmodup 10281 modaddmodlo 10282 modsumfzodifsn 10290 addmodlteq 10292 facubnd 10614 resqrexlemdecn 10907 modfsummodlemstep 11349 divcnv 11389 cvgratnnlemabsle 11419 fprodmodd 11533 efcllemp 11550 ege2le3 11563 eftlub 11582 eflegeo 11593 eirraplem 11668 dvdslelemd 11729 dvdsmod 11748 mulmoddvds 11749 divalgmod 11812 bezoutlemnewy 11874 bezoutlemstep 11875 sqgcd 11907 eucalglt 11928 qredeu 11968 prmind2 11991 nprm 11994 sqrt2irraplemnn 12048 divdenle 12066 qnumgt0 12067 hashdvds 12088 crth 12091 phimullem 12092 eulerthlema 12097 fermltl 12101 prmdiv 12102 prmdiveq 12103 |
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