| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∈ wcel 2106
‘cfv 6543 ℝcr 11108 ℝ+crp 12973 logclog 26062 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-rep 5285 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7724 ax-inf2 9635 ax-cnex 11165 ax-resscn 11166 ax-1cn 11167 ax-icn 11168 ax-addcl 11169 ax-addrcl 11170 ax-mulcl 11171 ax-mulrcl 11172 ax-mulcom 11173 ax-addass 11174 ax-mulass 11175 ax-distr 11176 ax-i2m1 11177 ax-1ne0 11178 ax-1rid 11179 ax-rnegex 11180 ax-rrecex 11181 ax-cnre 11182 ax-pre-lttri 11183 ax-pre-lttrn 11184 ax-pre-ltadd 11185 ax-pre-mulgt0 11186 ax-pre-sup 11187 ax-addf 11188 ax-mulf 11189 |
| This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3or 1088 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ne 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-rmo 3376 df-reu 3377 df-rab 3433 df-v 3476 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-tp 4633 df-op 4635 df-uni 4909 df-int 4951 df-iun 4999 df-iin 5000 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-se 5632 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-isom 6552 df-riota 7364 df-ov 7411 df-oprab 7412 df-mpo 7413 df-of 7669 df-om 7855 df-1st 7974 df-2nd 7975 df-supp 8146 df-frecs 8265 df-wrecs 8296 df-recs 8370 df-rdg 8409 df-1o 8465 df-2o 8466 df-er 8702 df-map 8821 df-pm 8822 df-ixp 8891 df-en 8939 df-dom 8940 df-sdom 8941 df-fin 8942 df-fsupp 9361 df-fi 9405 df-sup 9436 df-inf 9437 df-oi 9504 df-card 9933 df-pnf 11249 df-mnf 11250 df-xr 11251 df-ltxr 11252 df-le 11253 df-sub 11445 df-neg 11446 df-div 11871 df-nn 12212 df-2 12274
df-3 12275 df-4 12276
df-5 12277 df-6 12278
df-7 12279 df-8 12280
df-9 12281 df-n0 12472 df-z 12558
df-dec 12677 df-uz 12822 df-q 12932
df-rp 12974 df-xneg 13091 df-xadd 13092 df-xmul 13093 df-ioo 13327 df-ioc 13328 df-ico 13329 df-icc 13330 df-fz 13484 df-fzo 13627 df-fl 13756 df-mod 13834 df-seq 13966 df-exp 14027 df-fac 14233 df-bc 14262 df-hash 14290 df-shft 15013 df-cj 15045 df-re 15046 df-im 15047 df-sqrt 15181 df-abs 15182 df-limsup 15414 df-clim 15431 df-rlim 15432 df-sum 15632 df-ef 16010 df-sin 16012 df-cos 16013 df-pi 16015 df-struct 17079 df-sets 17096 df-slot 17114 df-ndx 17126 df-base 17144 df-ress 17173 df-plusg 17209 df-mulr 17210 df-starv 17211 df-sca 17212 df-vsca 17213 df-ip 17214 df-tset 17215 df-ple 17216 df-ds 17218 df-unif 17219 df-hom 17220 df-cco 17221 df-rest 17367 df-topn 17368 df-0g 17386 df-gsum 17387 df-topgen 17388 df-pt 17389 df-prds 17392 df-xrs 17447 df-qtop 17452 df-imas 17453 df-xps 17455 df-mre 17529 df-mrc 17530 df-acs 17532 df-mgm 18560 df-sgrp 18609 df-mnd 18625 df-submnd 18671 df-mulg 18950 df-cntz 19180 df-cmn 19649 df-psmet 20935 df-xmet 20936 df-met 20937 df-bl 20938 df-mopn 20939 df-fbas 20940 df-fg 20941 df-cnfld 20944 df-top 22395 df-topon 22412 df-topsp 22434 df-bases 22448 df-cld 22522 df-ntr 22523 df-cls 22524 df-nei 22601 df-lp 22639 df-perf 22640 df-cn 22730 df-cnp 22731 df-haus 22818 df-tx 23065 df-hmeo 23258 df-fil 23349 df-fm 23441 df-flim 23442 df-flf 23443 df-xms 23825 df-ms 23826 df-tms 23827 df-cncf 24393 df-limc 25382 df-dv 25383 df-log 26064 |
| This theorem is referenced by: logcnlem3
26151 advlogexp
26162 logccv
26170 recxpcl
26182 cxpsqrt
26210 loglesqrt
26263 logbrec
26284 logbleb
26285 logblt
26286 ang180lem2
26312 isosctrlem2
26321 atanlogaddlem
26415 atantan
26425 birthdaylem2
26454 birthdaylem3
26455 amgmlem
26491 emcllem1
26497 emcllem2
26498 emcllem3
26499 emcllem4
26500 emcllem5
26501 emcllem6
26502 harmonicubnd
26511 fsumharmonic
26513 zetacvg
26516 lgamgulmlem3
26532 lgamgulmlem4
26533 lgamgulmlem5
26534 lgamgulmlem6
26535 lgamgulm2
26537 lgambdd
26538 lgamcvg2
26556 gamcvg
26557 gamcvg2lem
26560 relgamcl
26563 lgam1
26565 chtf
26609 efchtcl
26612 chtge0
26613 vmacl
26619 chtprm
26654 chtdif
26659 efchtdvds
26660 prmorcht
26679 vmalelog
26705 chtleppi
26710 chtublem
26711 fsumvma2
26714 pclogsum
26715 vmasum
26716 chpval2
26718 chpchtsum
26719 chpub
26720 logfacubnd
26721 logfaclbnd
26722 logexprlim
26725 logfacrlim2
26726 bposlem1
26784 bposlem9
26792 chebbnd1lem1
26969 chebbnd1lem2
26970 chebbnd1lem3
26971 chtppilimlem1
26973 chpchtlim
26979 vmadivsum
26982 vmadivsumb
26983 rplogsumlem1
26984 rplogsumlem2
26985 rpvmasumlem
26987 dchrvmasumlem1
26995 dchrvmasum2lem
26996 dchrvmasum2if
26997 dchrvmasumlem2
26998 dchrvmasumiflem1
27001 dchrvmasumiflem2
27002 rplogsum
27027 mulogsumlem
27031 mulogsum
27032 mulog2sumlem1
27034 mulog2sumlem2
27035 mulog2sumlem3
27036 vmalogdivsum2
27038 vmalogdivsum
27039 2vmadivsumlem
27040 logsqvma
27042 logsqvma2
27043 log2sumbnd
27044 selberglem2
27046 selbergb
27049 selberg2lem
27050 selberg2b
27052 chpdifbndlem1
27053 chpdifbndlem2
27054 logdivbnd
27056 selberg3lem1
27057 selberg3lem2
27058 selberg3
27059 selberg4lem1
27060 selberg4
27061 selberg3r
27069 selberg4r
27070 selberg34r
27071 pntsf
27073 pntsval2
27076 pntrlog2bndlem1
27077 pntrlog2bndlem2
27078 pntrlog2bndlem3
27079 pntrlog2bndlem4
27080 pntrlog2bndlem5
27081 pntrlog2bndlem6
27083 pntrlog2bnd
27084 pntpbnd1a
27085 pntpbnd2
27087 pntibndlem2
27091 pntlemb
27097 pntlemg
27098 pntlemh
27099 pntlemn
27100 pntlemr
27102 pntlemj
27103 pntlemf
27105 pntlemk
27106 pntlemo
27107 ostth2lem4
27136 ostth2
27137 ostth3
27138 xrge0iifcnv
32908 xrge0iifiso
32910 xrge0iifhom
32912 hgt750lemd
33655 logdivsqrle
33657 hgt750lem
33658 hgt750lemb
33663 hgt750leme
33665 tgoldbachgtde
33667 dvrelogpow2b
40928 aks4d1p1p6
40933 aks4d1p1p7
40934 aks4d1p1p5
40935 aks4d1p6
40941 stirlinglem4
44783 stirlinglem11
44790 stirlinglem12
44791 stirlinglem13
44792 lighneallem2
46264 rege1logbrege0
47234 amgmwlem
47839 |
