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Mirrors > Home > MPE Home > Th. List > 1le1 | Structured version Visualization version GIF version |
Description: One is less than or equal to one. (Contributed by David A. Wheeler, 16-Jul-2016.) |
Ref | Expression |
---|---|
1le1 | ⊢ 1 ≤ 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1re 11089 | . 2 ⊢ 1 ∈ ℝ | |
2 | 1 | leidi 11623 | 1 ⊢ 1 ≤ 1 |
Colors of variables: wff setvar class |
Syntax hints: class class class wbr 5104 1c1 10986 ≤ cle 11124 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2709 ax-sep 5255 ax-nul 5262 ax-pow 5319 ax-pr 5383 ax-un 7663 ax-resscn 11042 ax-1cn 11043 ax-icn 11044 ax-addcl 11045 ax-mulcl 11047 ax-mulrcl 11048 ax-i2m1 11053 ax-1ne0 11054 ax-rrecex 11057 ax-cnre 11058 ax-pre-lttri 11059 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2540 df-eu 2569 df-clab 2716 df-cleq 2730 df-clel 2816 df-nfc 2888 df-ne 2943 df-nel 3049 df-ral 3064 df-rex 3073 df-rab 3407 df-v 3446 df-sbc 3739 df-csb 3855 df-dif 3912 df-un 3914 df-in 3916 df-ss 3926 df-nul 4282 df-if 4486 df-pw 4561 df-sn 4586 df-pr 4588 df-op 4592 df-uni 4865 df-br 5105 df-opab 5167 df-mpt 5188 df-id 5529 df-xp 5637 df-rel 5638 df-cnv 5639 df-co 5640 df-dm 5641 df-rn 5642 df-res 5643 df-ima 5644 df-iota 6444 df-fun 6494 df-fn 6495 df-f 6496 df-f1 6497 df-fo 6498 df-f1o 6499 df-fv 6500 df-ov 7353 df-er 8582 df-en 8818 df-dom 8819 df-sdom 8820 df-pnf 11125 df-mnf 11126 df-xr 11127 df-ltxr 11128 df-le 11129 |
This theorem is referenced by: nnge1 12115 1elunit 13317 fldiv4p1lem1div2 13670 expge1 13935 leexp1a 14008 bernneq 14059 faclbnd3 14121 facubnd 14129 hashsnle1 14246 wrdlen1 14371 wrdl1exs1 14430 fprodge1 15814 cos1bnd 16005 sincos1sgn 16011 eirrlem 16022 xrhmeo 24237 pcoval2 24307 pige3ALT 25804 cxplea 25979 cxple2a 25982 cxpaddlelem 26032 abscxpbnd 26034 mule1 26425 sqff1o 26459 logfacbnd3 26499 logexprlim 26501 dchrabs2 26538 bposlem5 26564 zabsle1 26572 lgslem2 26574 lgsfcl2 26579 lgseisen 26655 dchrisum0flblem1 26784 log2sumbnd 26820 clwwlknon1le1 28850 nmopun 30761 branmfn 30852 stge1i 30985 dstfrvunirn 32854 subfaclim 33562 sticksstones12a 40496 jm2.17a 41186 jm2.17b 41187 fmuldfeq 43615 stoweidlem3 44035 stoweidlem18 44050 sepfsepc 46751 seppcld 46753 |
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