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Mirrors > Home > MPE Home > Th. List > sumeq2sdv | Structured version Visualization version Unicode version |
Description: Equality deduction for sum. (Contributed by NM, 3-Jan-2006.) |
Ref | Expression |
---|---|
sumeq2sdv.1 |
Ref | Expression |
---|---|
sumeq2sdv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sumeq2sdv.1 | . . 3 | |
2 | 1 | adantr 481 | . 2 |
3 | 2 | sumeq2dv 14433 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 csu 14416 |
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-cnex 9992 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-mulcom 10000 ax-addass 10001 ax-mulass 10002 ax-distr 10003 ax-i2m1 10004 ax-1ne0 10005 ax-1rid 10006 ax-rnegex 10007 ax-rrecex 10008 ax-cnre 10009 ax-pre-lttri 10010 ax-pre-lttrn 10011 ax-pre-ltadd 10012 ax-pre-mulgt0 10013 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-fal 1489 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-reu 2919 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-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-tr 4753 df-id 5024 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 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-pred 5680 df-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 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-riota 6611 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-om 7066 df-1st 7168 df-2nd 7169 df-wrecs 7407 df-recs 7468 df-rdg 7506 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 df-sub 10268 df-neg 10269 df-nn 11021 df-n0 11293 df-z 11378 df-uz 11688 df-fz 12327 df-seq 12802 df-sum 14417 |
This theorem is referenced by: sumsplit 14499 fsumrlim 14543 incexclem 14568 bpolylem 14779 bpolyval 14780 efval 14810 rpnnen2lem12 14954 pcfac 15603 ramcl 15733 cshwshashnsame 15810 fsumcn 22673 fsum2cn 22674 lebnumlem3 22762 uniioombllem6 23356 itg1climres 23481 itgeq1f 23538 itgeq2 23544 dvmptfsum 23738 elplyr 23957 plyeq0lem 23966 plyadd 23973 plymul 23974 coeeu 23981 coelem 23982 coeeq 23983 coeidlem 23993 coeid 23994 coeid2 23995 plyco 23997 plycjlem 24032 aareccl 24081 taylply2 24122 pserdvlem2 24182 pserdv 24183 abelthlem6 24190 abelthlem9 24194 logtayl 24406 leibpi 24669 basellem3 24809 dchrvmasum2if 25186 dchrvmaeq0 25193 rpvmasum2 25201 dchrisum0re 25202 brcgr 25780 axsegcon 25807 dipfval 27557 ipval 27558 fsumiunle 29575 itgeq12dv 30388 eulerpartleme 30425 eulerpartlemr 30436 eulerpartlemn 30443 reprsum 30691 reprsuc 30693 reprpmtf1o 30704 vtsval 30715 iprodgam 31628 fwddifnval 32270 knoppndvlem6 32508 knoppf 32526 rrnmval 33627 fsumshftd 34237 fsumcnf 39180 dvmptfprod 40160 stoweidlem17 40234 stoweidlem26 40243 stoweidlem30 40247 stoweidlem32 40249 dirkertrigeq 40318 dirkeritg 40319 fourierdlem83 40406 fourierdlem103 40426 etransclem46 40497 nnsum3primes4 41676 nnsum4primesodd 41684 nnsum4primesoddALTV 41685 nnsum4primesevenALTV 41689 nn0sumshdiglemB 42414 nn0sumshdiglem1 42415 aacllem 42547 |
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