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Mirrors > Home > MPE Home > Th. List > lelttr | Structured version Visualization version Unicode version |
Description: Transitive law. (Contributed by NM, 23-May-1999.) |
Ref | Expression |
---|---|
lelttr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leloe 10124 | . . . 4 | |
2 | 1 | 3adant3 1081 | . . 3 |
3 | lttr 10114 | . . . . 5 | |
4 | 3 | expd 452 | . . . 4 |
5 | breq1 4656 | . . . . . 6 | |
6 | 5 | biimprd 238 | . . . . 5 |
7 | 6 | a1i 11 | . . . 4 |
8 | 4, 7 | jaod 395 | . . 3 |
9 | 2, 8 | sylbid 230 | . 2 |
10 | 9 | impd 447 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wo 383 wa 384 w3a 1037 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 ax-pre-lttrn 10011 |
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: letr 10131 lelttri 10164 lelttrd 10195 letrp1 10865 ltmul12a 10879 ledivp1 10925 supmul1 10992 bndndx 11291 uzind 11469 fnn0ind 11476 rpnnen1lem5 11818 rpnnen1lem5OLD 11824 xrinfmsslem 12138 elfzo0z 12509 nn0p1elfzo 12510 fzofzim 12514 elfzodifsumelfzo 12533 flge 12606 flflp1 12608 flltdivnn0lt 12634 modfzo0difsn 12742 fsequb 12774 expnlbnd2 12995 ccat2s1fvw 13415 swrdswrd 13460 swrdccatin12lem3 13490 repswswrd 13531 caubnd2 14097 caubnd 14098 mulcn2 14326 cn1lem 14328 rlimo1 14347 o1rlimmul 14349 climsqz 14371 climsqz2 14372 rlimsqzlem 14379 climsup 14400 caucvgrlem2 14405 iseralt 14415 cvgcmp 14548 cvgcmpce 14550 ruclem3 14962 ruclem12 14970 ltoddhalfle 15085 algcvgblem 15290 ncoprmlnprm 15436 pclem 15543 infpn2 15617 gsummoncoe1 19674 mp2pm2mplem4 20614 metss2lem 22316 ngptgp 22440 nghmcn 22549 iocopnst 22739 ovollb2lem 23256 ovolicc2lem4 23288 volcn 23374 ismbf3d 23421 dvcnvrelem1 23780 dvfsumrlim 23794 ulmcn 24153 mtest 24158 logdivlti 24366 isosctrlem1 24548 ftalem2 24800 chtub 24937 bposlem6 25014 gausslemma2dlem2 25092 chtppilim 25164 dchrisumlem3 25180 pntlem3 25298 clwlkclwwlklem2a 26899 vacn 27549 nmcvcn 27550 blocni 27660 chscllem2 28497 lnconi 28892 staddi 29105 stadd3i 29107 ltflcei 33397 poimirlem29 33438 geomcau 33555 heibor1lem 33608 bfplem2 33622 rrncmslem 33631 climinf 39838 leltletr 41308 zm1nn 41316 iccpartigtl 41359 tgoldbach 41705 tgoldbachOLD 41712 ply1mulgsumlem2 42175 difmodm1lt 42317 |
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