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Mirrors > Home > ILE Home > Th. List > 0le1 | Unicode version |
Description: 0 is less than or equal to 1. (Contributed by Mario Carneiro, 29-Apr-2015.) |
Ref | Expression |
---|---|
0le1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0re 7890 | . 2 | |
2 | 1re 7889 | . 2 | |
3 | 0lt1 8016 | . 2 | |
4 | 1, 2, 3 | ltleii 7992 | 1 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3976 cc0 7744 c1 7745 cle 7925 |
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-rnegex 7853 ax-pre-ltirr 7856 ax-pre-lttrn 7858 |
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-br 3977 df-opab 4038 df-xp 4604 df-cnv 4606 df-pnf 7926 df-mnf 7927 df-xr 7928 df-ltxr 7929 df-le 7930 |
This theorem is referenced by: lemulge11 8752 sup3exmid 8843 0le2 8938 1eluzge0 9503 0elunit 9913 1elunit 9914 fldiv4p1lem1div2 10230 q1mod 10281 expge0 10481 expge1 10482 faclbnd3 10645 sqrt1 10974 sqrt2gt1lt2 10977 abs1 11000 cvgratnnlembern 11450 fprodge0 11564 fprodge1 11566 ege2le3 11598 sinbnd 11679 cosbnd 11680 cos2bnd 11687 nn0oddm1d2 11831 flodddiv4 11856 sqnprm 12047 isprm5lem 12052 sqrt2irrap 12091 nn0sqrtelqelz 12117 pythagtriplem3 12178 sinhalfpilem 13259 trilpolemclim 13756 trilpolemlt1 13761 nconstwlpolemgt0 13783 |
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