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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 7766 | . 2 | |
2 | 1re 7765 | . 2 | |
3 | 0lt1 7889 | . 2 | |
4 | 1, 2, 3 | ltleii 7866 | 1 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3929 cc0 7620 c1 7621 cle 7801 |
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-rnegex 7729 ax-pre-ltirr 7732 ax-pre-lttrn 7734 |
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-br 3930 df-opab 3990 df-xp 4545 df-cnv 4547 df-pnf 7802 df-mnf 7803 df-xr 7804 df-ltxr 7805 df-le 7806 |
This theorem is referenced by: lemulge11 8624 sup3exmid 8715 0le2 8810 1eluzge0 9369 0elunit 9769 1elunit 9770 fldiv4p1lem1div2 10078 q1mod 10129 expge0 10329 expge1 10330 faclbnd3 10489 sqrt1 10818 sqrt2gt1lt2 10821 abs1 10844 cvgratnnlembern 11292 ege2le3 11377 sinbnd 11459 cosbnd 11460 cos2bnd 11467 nn0oddm1d2 11606 flodddiv4 11631 sqnprm 11816 sqrt2irrap 11858 nn0sqrtelqelz 11884 sinhalfpilem 12872 trilpolemclim 13229 trilpolemlt1 13234 |
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