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Mirrors > Home > MPE Home > Th. List > leloed | Structured version Visualization version Unicode version |
Description: 'Less than or equal to' in terms of 'less than'. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
ltd.1 | |
ltd.2 |
Ref | Expression |
---|---|
leloed |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltd.1 | . 2 | |
2 | ltd.2 | . 2 | |
3 | leloe 10124 | . 2 | |
4 | 1, 2, 3 | syl2anc 693 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wo 383 wceq 1483 wcel 1990 class class class wbr 4653 cr 9935 clt 10074 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-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-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: mulge0 10546 prodgt0 10868 lemul1 10875 supfirege 11009 nn0le2is012 11441 nn0o1gt2 15097 reconnlem1 22629 reconnlem2 22630 ivthle 23225 ivthle2 23226 ovolicc2lem3 23287 itgsplitioo 23604 dvlip 23756 dvge0 23769 dvfsumlem1 23789 dgrco 24031 plydivex 24052 coseq00topi 24254 logreclem 24500 scvxcvx 24712 pntrlog2bndlem5 25270 dnibndlem13 32480 elpell1qr2 37436 pellfundex 37450 fmul01lt1lem2 39817 wallispilem3 40284 fourierdlem25 40349 fourierdlem42 40366 lighneallem4b 41526 nn0o1gt2ALTV 41605 stgoldbwt 41664 sbgoldbwt 41665 sbgoldbalt 41669 nnsum3primesle9 41682 bgoldbtbndlem1 41693 |
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