Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nnnlt1 | Unicode version |
Description: A positive integer is not less than one. (Contributed by NM, 18-Jan-2004.) (Revised by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
nnnlt1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnge1 8856 | . 2 | |
2 | 1re 7877 | . . 3 | |
3 | nnre 8840 | . . 3 | |
4 | lenlt 7953 | . . 3 | |
5 | 2, 3, 4 | sylancr 411 | . 2 |
6 | 1, 5 | mpbid 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wcel 2128 class class class wbr 3965 cr 7731 c1 7733 clt 7912 cle 7913 cn 8833 |
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 4496 ax-cnex 7823 ax-resscn 7824 ax-1re 7826 ax-addrcl 7829 ax-0lt1 7838 ax-0id 7840 ax-rnegex 7841 ax-pre-ltirr 7844 ax-pre-lttrn 7846 ax-pre-ltadd 7848 |
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 4592 df-cnv 4594 df-iota 5135 df-fv 5178 df-ov 5827 df-pnf 7914 df-mnf 7915 df-xr 7916 df-ltxr 7917 df-le 7918 df-inn 8834 |
This theorem is referenced by: 0nnn 8860 nnsub 8872 indstr 9504 indstr2 9520 sqrt2irr 12036 |
Copyright terms: Public domain | W3C validator |