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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0re 7954 |
. 2
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2 | 1re 7953 |
. 2
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3 | 0lt1 8080 |
. 2
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4 | 1, 2, 3 | ltleii 8056 |
1
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Colors of variables: wff set class |
Syntax hints: class class
class wbr 4002 ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4120 ax-pow 4173 ax-pr 4208 ax-un 4432 ax-setind 4535 ax-cnex 7899 ax-resscn 7900 ax-1re 7902 ax-addrcl 7905 ax-0lt1 7914 ax-rnegex 7917 ax-pre-ltirr 7920 ax-pre-lttrn 7922 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-opab 4064 df-xp 4631 df-cnv 4633 df-pnf 7990 df-mnf 7991 df-xr 7992 df-ltxr 7993 df-le 7994 |
This theorem is referenced by: lemulge11 8819 sup3exmid 8910 0le2 9005 1eluzge0 9570 0elunit 9982 1elunit 9983 fldiv4p1lem1div2 10300 q1mod 10351 expge0 10551 expge1 10552 faclbnd3 10716 sqrt1 11048 sqrt2gt1lt2 11051 abs1 11074 cvgratnnlembern 11524 fprodge0 11638 fprodge1 11640 ege2le3 11672 sinbnd 11753 cosbnd 11754 cos2bnd 11761 nn0oddm1d2 11906 flodddiv4 11931 sqnprm 12128 isprm5lem 12133 sqrt2irrap 12172 nn0sqrtelqelz 12198 pythagtriplem3 12259 sinhalfpilem 14083 zabsle1 14271 lgslem2 14273 lgsfcl2 14278 lgsdir2lem1 14300 lgsne0 14310 lgsdinn0 14320 trilpolemclim 14644 trilpolemlt1 14649 nconstwlpolemgt0 14671 |
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