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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 10629 | . 2 ⊢ 1 ∈ ℝ | |
2 | 1 | leidi 11162 | 1 ⊢ 1 ≤ 1 |
Colors of variables: wff setvar class |
Syntax hints: class class class wbr 5057 1c1 10526 ≤ cle 10664 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pow 5257 ax-pr 5320 ax-un 7450 ax-resscn 10582 ax-1cn 10583 ax-icn 10584 ax-addcl 10585 ax-mulcl 10587 ax-mulrcl 10588 ax-i2m1 10593 ax-1ne0 10594 ax-rrecex 10597 ax-cnre 10598 ax-pre-lttri 10599 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ne 3014 df-nel 3121 df-ral 3140 df-rex 3141 df-rab 3144 df-v 3494 df-sbc 3770 df-csb 3881 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-pw 4537 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-opab 5120 df-mpt 5138 df-id 5453 df-xp 5554 df-rel 5555 df-cnv 5556 df-co 5557 df-dm 5558 df-rn 5559 df-res 5560 df-ima 5561 df-iota 6307 df-fun 6350 df-fn 6351 df-f 6352 df-f1 6353 df-fo 6354 df-f1o 6355 df-fv 6356 df-ov 7148 df-er 8278 df-en 8498 df-dom 8499 df-sdom 8500 df-pnf 10665 df-mnf 10666 df-xr 10667 df-ltxr 10668 df-le 10669 |
This theorem is referenced by: nnge1 11653 1elunit 12844 fldiv4p1lem1div2 13193 expge1 13454 leexp1a 13527 bernneq 13578 faclbnd3 13640 facubnd 13648 hashsnle1 13766 wrdlen1 13894 wrdl1exs1 13955 fprodge1 15337 cos1bnd 15528 sincos1sgn 15534 eirrlem 15545 xrhmeo 23477 pcoval2 23547 pige3ALT 25032 cxplea 25206 cxple2a 25209 cxpaddlelem 25259 abscxpbnd 25261 mule1 25652 sqff1o 25686 logfacbnd3 25726 logexprlim 25728 dchrabs2 25765 bposlem5 25791 zabsle1 25799 lgslem2 25801 lgsfcl2 25806 lgseisen 25882 dchrisum0flblem1 26011 log2sumbnd 26047 clwwlknon1le1 27807 nmopun 29718 branmfn 29809 stge1i 29942 dstfrvunirn 31631 subfaclim 32332 jm2.17a 39435 jm2.17b 39436 fmuldfeq 41740 stoweidlem3 42165 stoweidlem18 42180 |
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