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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 11262 | . 2 ⊢ 1 ∈ ℝ | |
| 2 | 1 | leidi 11798 | 1 ⊢ 1 ≤ 1 | 
| Colors of variables: wff setvar class | 
| Syntax hints: class class class wbr 5142 1c1 11157 ≤ cle 11297 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-10 2140 ax-11 2156 ax-12 2176 ax-ext 2707 ax-sep 5295 ax-nul 5305 ax-pow 5364 ax-pr 5431 ax-un 7756 ax-resscn 11213 ax-1cn 11214 ax-icn 11215 ax-addcl 11216 ax-mulcl 11218 ax-mulrcl 11219 ax-i2m1 11224 ax-1ne0 11225 ax-rrecex 11228 ax-cnre 11229 ax-pre-lttri 11230 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1779 df-nf 1783 df-sb 2064 df-mo 2539 df-eu 2568 df-clab 2714 df-cleq 2728 df-clel 2815 df-nfc 2891 df-ne 2940 df-nel 3046 df-ral 3061 df-rex 3070 df-rab 3436 df-v 3481 df-sbc 3788 df-csb 3899 df-dif 3953 df-un 3955 df-in 3957 df-ss 3967 df-nul 4333 df-if 4525 df-pw 4601 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4907 df-br 5143 df-opab 5205 df-mpt 5225 df-id 5577 df-xp 5690 df-rel 5691 df-cnv 5692 df-co 5693 df-dm 5694 df-rn 5695 df-res 5696 df-ima 5697 df-iota 6513 df-fun 6562 df-fn 6563 df-f 6564 df-f1 6565 df-fo 6566 df-f1o 6567 df-fv 6568 df-ov 7435 df-er 8746 df-en 8987 df-dom 8988 df-sdom 8989 df-pnf 11298 df-mnf 11299 df-xr 11300 df-ltxr 11301 df-le 11302 | 
| This theorem is referenced by: nnge1 12295 1elunit 13511 fldiv4p1lem1div2 13876 expge1 14141 leexp1a 14216 bernneq 14269 faclbnd3 14332 facubnd 14340 hashsnle1 14457 wrdlen1 14593 wrdl1exs1 14652 fprodge1 16032 cos1bnd 16224 sincos1sgn 16230 eirrlem 16241 psdmvr 22174 xrhmeo 24978 pcoval2 25050 pige3ALT 26563 cxplea 26739 cxple2a 26742 cxpaddlelem 26795 abscxpbnd 26797 mule1 27192 sqff1o 27226 logfacbnd3 27268 logexprlim 27270 dchrabs2 27307 bposlem5 27333 zabsle1 27341 lgslem2 27343 lgsfcl2 27348 lgseisen 27424 dchrisum0flblem1 27553 log2sumbnd 27589 clwwlknon1le1 30121 nmopun 32034 branmfn 32125 stge1i 32258 dstfrvunirn 34478 subfaclim 35194 sticksstones12a 42159 jm2.17a 42977 jm2.17b 42978 fmuldfeq 45603 stoweidlem3 46023 stoweidlem18 46038 m1modne 47355 sepfsepc 48832 seppcld 48834 | 
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