| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∈ wcel 2106
‘cfv 6543 ℝcr 11111 ℝ+crp 12976 logclog 26070 |
| 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 7727 ax-inf2 9638 ax-cnex 11168 ax-resscn 11169 ax-1cn 11170 ax-icn 11171 ax-addcl 11172 ax-addrcl 11173 ax-mulcl 11174 ax-mulrcl 11175 ax-mulcom 11176 ax-addass 11177 ax-mulass 11178 ax-distr 11179 ax-i2m1 11180 ax-1ne0 11181 ax-1rid 11182 ax-rnegex 11183 ax-rrecex 11184 ax-cnre 11185 ax-pre-lttri 11186 ax-pre-lttrn 11187 ax-pre-ltadd 11188 ax-pre-mulgt0 11189 ax-pre-sup 11190 ax-addf 11191 ax-mulf 11192 |
| 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 7367 df-ov 7414 df-oprab 7415 df-mpo 7416 df-of 7672 df-om 7858 df-1st 7977 df-2nd 7978 df-supp 8149 df-frecs 8268 df-wrecs 8299 df-recs 8373 df-rdg 8412 df-1o 8468 df-2o 8469 df-er 8705 df-map 8824 df-pm 8825 df-ixp 8894 df-en 8942 df-dom 8943 df-sdom 8944 df-fin 8945 df-fsupp 9364 df-fi 9408 df-sup 9439 df-inf 9440 df-oi 9507 df-card 9936 df-pnf 11252 df-mnf 11253 df-xr 11254 df-ltxr 11255 df-le 11256 df-sub 11448 df-neg 11449 df-div 11874 df-nn 12215 df-2 12277
df-3 12278 df-4 12279
df-5 12280 df-6 12281
df-7 12282 df-8 12283
df-9 12284 df-n0 12475 df-z 12561
df-dec 12680 df-uz 12825 df-q 12935
df-rp 12977 df-xneg 13094 df-xadd 13095 df-xmul 13096 df-ioo 13330 df-ioc 13331 df-ico 13332 df-icc 13333 df-fz 13487 df-fzo 13630 df-fl 13759 df-mod 13837 df-seq 13969 df-exp 14030 df-fac 14236 df-bc 14265 df-hash 14293 df-shft 15016 df-cj 15048 df-re 15049 df-im 15050 df-sqrt 15184 df-abs 15185 df-limsup 15417 df-clim 15434 df-rlim 15435 df-sum 15635 df-ef 16013 df-sin 16015 df-cos 16016 df-pi 16018 df-struct 17082 df-sets 17099 df-slot 17117 df-ndx 17129 df-base 17147 df-ress 17176 df-plusg 17212 df-mulr 17213 df-starv 17214 df-sca 17215 df-vsca 17216 df-ip 17217 df-tset 17218 df-ple 17219 df-ds 17221 df-unif 17222 df-hom 17223 df-cco 17224 df-rest 17370 df-topn 17371 df-0g 17389 df-gsum 17390 df-topgen 17391 df-pt 17392 df-prds 17395 df-xrs 17450 df-qtop 17455 df-imas 17456 df-xps 17458 df-mre 17532 df-mrc 17533 df-acs 17535 df-mgm 18563 df-sgrp 18612 df-mnd 18628 df-submnd 18674 df-mulg 18953 df-cntz 19183 df-cmn 19652 df-psmet 20942 df-xmet 20943 df-met 20944 df-bl 20945 df-mopn 20946 df-fbas 20947 df-fg 20948 df-cnfld 20951 df-top 22403 df-topon 22420 df-topsp 22442 df-bases 22456 df-cld 22530 df-ntr 22531 df-cls 22532 df-nei 22609 df-lp 22647 df-perf 22648 df-cn 22738 df-cnp 22739 df-haus 22826 df-tx 23073 df-hmeo 23266 df-fil 23357 df-fm 23449 df-flim 23450 df-flf 23451 df-xms 23833 df-ms 23834 df-tms 23835 df-cncf 24401 df-limc 25390 df-dv 25391 df-log 26072 |
| This theorem is referenced by: logcnlem3
26159 advlogexp
26170 logccv
26178 recxpcl
26190 cxpsqrt
26218 loglesqrt
26273 logbrec
26294 logbleb
26295 logblt
26296 ang180lem2
26322 isosctrlem2
26331 atanlogaddlem
26425 atantan
26435 birthdaylem2
26464 birthdaylem3
26465 amgmlem
26501 emcllem1
26507 emcllem2
26508 emcllem3
26509 emcllem4
26510 emcllem5
26511 emcllem6
26512 harmonicubnd
26521 fsumharmonic
26523 zetacvg
26526 lgamgulmlem3
26542 lgamgulmlem4
26543 lgamgulmlem5
26544 lgamgulmlem6
26545 lgamgulm2
26547 lgambdd
26548 lgamcvg2
26566 gamcvg
26567 gamcvg2lem
26570 relgamcl
26573 lgam1
26575 chtf
26619 efchtcl
26622 chtge0
26623 vmacl
26629 chtprm
26664 chtdif
26669 efchtdvds
26670 prmorcht
26689 vmalelog
26715 chtleppi
26720 chtublem
26721 fsumvma2
26724 pclogsum
26725 vmasum
26726 chpval2
26728 chpchtsum
26729 chpub
26730 logfacubnd
26731 logfaclbnd
26732 logexprlim
26735 logfacrlim2
26736 bposlem1
26794 bposlem9
26802 chebbnd1lem1
26979 chebbnd1lem2
26980 chebbnd1lem3
26981 chtppilimlem1
26983 chpchtlim
26989 vmadivsum
26992 vmadivsumb
26993 rplogsumlem1
26994 rplogsumlem2
26995 rpvmasumlem
26997 dchrvmasumlem1
27005 dchrvmasum2lem
27006 dchrvmasum2if
27007 dchrvmasumlem2
27008 dchrvmasumiflem1
27011 dchrvmasumiflem2
27012 rplogsum
27037 mulogsumlem
27041 mulogsum
27042 mulog2sumlem1
27044 mulog2sumlem2
27045 mulog2sumlem3
27046 vmalogdivsum2
27048 vmalogdivsum
27049 2vmadivsumlem
27050 logsqvma
27052 logsqvma2
27053 log2sumbnd
27054 selberglem2
27056 selbergb
27059 selberg2lem
27060 selberg2b
27062 chpdifbndlem1
27063 chpdifbndlem2
27064 logdivbnd
27066 selberg3lem1
27067 selberg3lem2
27068 selberg3
27069 selberg4lem1
27070 selberg4
27071 selberg3r
27079 selberg4r
27080 selberg34r
27081 pntsf
27083 pntsval2
27086 pntrlog2bndlem1
27087 pntrlog2bndlem2
27088 pntrlog2bndlem3
27089 pntrlog2bndlem4
27090 pntrlog2bndlem5
27091 pntrlog2bndlem6
27093 pntrlog2bnd
27094 pntpbnd1a
27095 pntpbnd2
27097 pntibndlem2
27101 pntlemb
27107 pntlemg
27108 pntlemh
27109 pntlemn
27110 pntlemr
27112 pntlemj
27113 pntlemf
27115 pntlemk
27116 pntlemo
27117 ostth2lem4
27146 ostth2
27147 ostth3
27148 xrge0iifcnv
32982 xrge0iifiso
32984 xrge0iifhom
32986 hgt750lemd
33729 logdivsqrle
33731 hgt750lem
33732 hgt750lemb
33737 hgt750leme
33739 tgoldbachgtde
33741 dvrelogpow2b
41019 aks4d1p1p6
41024 aks4d1p1p7
41025 aks4d1p1p5
41026 aks4d1p6
41032 stirlinglem4
44872 stirlinglem11
44879 stirlinglem12
44880 stirlinglem13
44881 lighneallem2
46353 rege1logbrege0
47322 amgmwlem
47927 |
