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Mirrors > Home > MPE Home > Th. List > 1le1 | Structured version Visualization version GIF version |
Description: 1 ≤ 1. Common special case. (Contributed by David A. Wheeler, 16-Jul-2016.) |
Ref | Expression |
---|---|
1le1 | ⊢ 1 ≤ 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1re 10039 | . 2 ⊢ 1 ∈ ℝ | |
2 | 1 | leidi 10562 | 1 ⊢ 1 ≤ 1 |
Colors of variables: wff setvar class |
Syntax hints: class class class wbr 4653 1c1 9937 ≤ cle 10075 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-mulcl 9998 ax-mulrcl 9999 ax-i2m1 10004 ax-1ne0 10005 ax-rrecex 10008 ax-cnre 10009 ax-pre-lttri 10010 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-nel 2898 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-xr 10078 df-ltxr 10079 df-le 10080 |
This theorem is referenced by: nnge1 11046 1elunit 12291 fldiv4p1lem1div2 12636 expge1 12897 leexp1a 12919 bernneq 12990 faclbnd3 13079 facubnd 13087 hashsnle1 13205 wrdlen1 13343 wrdl1exs1 13393 fprodge1 14726 cos1bnd 14917 sincos1sgn 14923 eirrlem 14932 xrhmeo 22745 pcoval2 22816 pige3 24269 cxplea 24442 cxple2a 24445 cxpaddlelem 24492 abscxpbnd 24494 mule1 24874 sqff1o 24908 logfacbnd3 24948 logexprlim 24950 dchrabs2 24987 bposlem5 25013 zabsle1 25021 lgslem2 25023 lgsfcl2 25028 lgseisen 25104 dchrisum0flblem1 25197 log2sumbnd 25233 nmopun 28873 branmfn 28964 stge1i 29097 dstfrvunirn 30536 subfaclim 31170 jm2.17a 37527 jm2.17b 37528 fmuldfeq 39815 stoweidlem3 40220 stoweidlem18 40235 |
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