| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∈ wcel 2107
‘cfv 6544 ℝcr 11109 ℝ+crp 12974 logclog 26063 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-rep 5286 ax-sep 5300 ax-nul 5307 ax-pow 5364 ax-pr 5428 ax-un 7725 ax-inf2 9636 ax-cnex 11166 ax-resscn 11167 ax-1cn 11168 ax-icn 11169 ax-addcl 11170 ax-addrcl 11171 ax-mulcl 11172 ax-mulrcl 11173 ax-mulcom 11174 ax-addass 11175 ax-mulass 11176 ax-distr 11177 ax-i2m1 11178 ax-1ne0 11179 ax-1rid 11180 ax-rnegex 11181 ax-rrecex 11182 ax-cnre 11183 ax-pre-lttri 11184 ax-pre-lttrn 11185 ax-pre-ltadd 11186 ax-pre-mulgt0 11187 ax-pre-sup 11188 ax-addf 11189 ax-mulf 11190 |
| This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-nel 3048 df-ral 3063 df-rex 3072 df-rmo 3377 df-reu 3378 df-rab 3434 df-v 3477 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-pss 3968 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-tp 4634 df-op 4636 df-uni 4910 df-int 4952 df-iun 5000 df-iin 5001 df-br 5150 df-opab 5212 df-mpt 5233 df-tr 5267 df-id 5575 df-eprel 5581 df-po 5589 df-so 5590 df-fr 5632 df-se 5633 df-we 5634 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-pred 6301 df-ord 6368 df-on 6369 df-lim 6370 df-suc 6371 df-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-f1 6549 df-fo 6550 df-f1o 6551 df-fv 6552 df-isom 6553 df-riota 7365 df-ov 7412 df-oprab 7413 df-mpo 7414 df-of 7670 df-om 7856 df-1st 7975 df-2nd 7976 df-supp 8147 df-frecs 8266 df-wrecs 8297 df-recs 8371 df-rdg 8410 df-1o 8466 df-2o 8467 df-er 8703 df-map 8822 df-pm 8823 df-ixp 8892 df-en 8940 df-dom 8941 df-sdom 8942 df-fin 8943 df-fsupp 9362 df-fi 9406 df-sup 9437 df-inf 9438 df-oi 9505 df-card 9934 df-pnf 11250 df-mnf 11251 df-xr 11252 df-ltxr 11253 df-le 11254 df-sub 11446 df-neg 11447 df-div 11872 df-nn 12213 df-2 12275
df-3 12276 df-4 12277
df-5 12278 df-6 12279
df-7 12280 df-8 12281
df-9 12282 df-n0 12473 df-z 12559
df-dec 12678 df-uz 12823 df-q 12933
df-rp 12975 df-xneg 13092 df-xadd 13093 df-xmul 13094 df-ioo 13328 df-ioc 13329 df-ico 13330 df-icc 13331 df-fz 13485 df-fzo 13628 df-fl 13757 df-mod 13835 df-seq 13967 df-exp 14028 df-fac 14234 df-bc 14263 df-hash 14291 df-shft 15014 df-cj 15046 df-re 15047 df-im 15048 df-sqrt 15182 df-abs 15183 df-limsup 15415 df-clim 15432 df-rlim 15433 df-sum 15633 df-ef 16011 df-sin 16013 df-cos 16014 df-pi 16016 df-struct 17080 df-sets 17097 df-slot 17115 df-ndx 17127 df-base 17145 df-ress 17174 df-plusg 17210 df-mulr 17211 df-starv 17212 df-sca 17213 df-vsca 17214 df-ip 17215 df-tset 17216 df-ple 17217 df-ds 17219 df-unif 17220 df-hom 17221 df-cco 17222 df-rest 17368 df-topn 17369 df-0g 17387 df-gsum 17388 df-topgen 17389 df-pt 17390 df-prds 17393 df-xrs 17448 df-qtop 17453 df-imas 17454 df-xps 17456 df-mre 17530 df-mrc 17531 df-acs 17533 df-mgm 18561 df-sgrp 18610 df-mnd 18626 df-submnd 18672 df-mulg 18951 df-cntz 19181 df-cmn 19650 df-psmet 20936 df-xmet 20937 df-met 20938 df-bl 20939 df-mopn 20940 df-fbas 20941 df-fg 20942 df-cnfld 20945 df-top 22396 df-topon 22413 df-topsp 22435 df-bases 22449 df-cld 22523 df-ntr 22524 df-cls 22525 df-nei 22602 df-lp 22640 df-perf 22641 df-cn 22731 df-cnp 22732 df-haus 22819 df-tx 23066 df-hmeo 23259 df-fil 23350 df-fm 23442 df-flim 23443 df-flf 23444 df-xms 23826 df-ms 23827 df-tms 23828 df-cncf 24394 df-limc 25383 df-dv 25384 df-log 26065 |
| This theorem is referenced by: logcnlem3
26152 advlogexp
26163 logccv
26171 recxpcl
26183 cxpsqrt
26211 loglesqrt
26266 logbrec
26287 logbleb
26288 logblt
26289 ang180lem2
26315 isosctrlem2
26324 atanlogaddlem
26418 atantan
26428 birthdaylem2
26457 birthdaylem3
26458 amgmlem
26494 emcllem1
26500 emcllem2
26501 emcllem3
26502 emcllem4
26503 emcllem5
26504 emcllem6
26505 harmonicubnd
26514 fsumharmonic
26516 zetacvg
26519 lgamgulmlem3
26535 lgamgulmlem4
26536 lgamgulmlem5
26537 lgamgulmlem6
26538 lgamgulm2
26540 lgambdd
26541 lgamcvg2
26559 gamcvg
26560 gamcvg2lem
26563 relgamcl
26566 lgam1
26568 chtf
26612 efchtcl
26615 chtge0
26616 vmacl
26622 chtprm
26657 chtdif
26662 efchtdvds
26663 prmorcht
26682 vmalelog
26708 chtleppi
26713 chtublem
26714 fsumvma2
26717 pclogsum
26718 vmasum
26719 chpval2
26721 chpchtsum
26722 chpub
26723 logfacubnd
26724 logfaclbnd
26725 logexprlim
26728 logfacrlim2
26729 bposlem1
26787 bposlem9
26795 chebbnd1lem1
26972 chebbnd1lem2
26973 chebbnd1lem3
26974 chtppilimlem1
26976 chpchtlim
26982 vmadivsum
26985 vmadivsumb
26986 rplogsumlem1
26987 rplogsumlem2
26988 rpvmasumlem
26990 dchrvmasumlem1
26998 dchrvmasum2lem
26999 dchrvmasum2if
27000 dchrvmasumlem2
27001 dchrvmasumiflem1
27004 dchrvmasumiflem2
27005 rplogsum
27030 mulogsumlem
27034 mulogsum
27035 mulog2sumlem1
27037 mulog2sumlem2
27038 mulog2sumlem3
27039 vmalogdivsum2
27041 vmalogdivsum
27042 2vmadivsumlem
27043 logsqvma
27045 logsqvma2
27046 log2sumbnd
27047 selberglem2
27049 selbergb
27052 selberg2lem
27053 selberg2b
27055 chpdifbndlem1
27056 chpdifbndlem2
27057 logdivbnd
27059 selberg3lem1
27060 selberg3lem2
27061 selberg3
27062 selberg4lem1
27063 selberg4
27064 selberg3r
27072 selberg4r
27073 selberg34r
27074 pntsf
27076 pntsval2
27079 pntrlog2bndlem1
27080 pntrlog2bndlem2
27081 pntrlog2bndlem3
27082 pntrlog2bndlem4
27083 pntrlog2bndlem5
27084 pntrlog2bndlem6
27086 pntrlog2bnd
27087 pntpbnd1a
27088 pntpbnd2
27090 pntibndlem2
27094 pntlemb
27100 pntlemg
27101 pntlemh
27102 pntlemn
27103 pntlemr
27105 pntlemj
27106 pntlemf
27108 pntlemk
27109 pntlemo
27110 ostth2lem4
27139 ostth2
27140 ostth3
27141 xrge0iifcnv
32913 xrge0iifiso
32915 xrge0iifhom
32917 hgt750lemd
33660 logdivsqrle
33662 hgt750lem
33663 hgt750lemb
33668 hgt750leme
33670 tgoldbachgtde
33672 dvrelogpow2b
40933 aks4d1p1p6
40938 aks4d1p1p7
40939 aks4d1p1p5
40940 aks4d1p6
40946 stirlinglem4
44793 stirlinglem11
44800 stirlinglem12
44801 stirlinglem13
44802 lighneallem2
46274 rege1logbrege0
47244 amgmwlem
47849 |
