Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2107
‘cfv 6497 ℝcr 11055 ℝ+crp 12920 logclog 25926 |
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 5243 ax-sep 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-inf2 9582 ax-cnex 11112 ax-resscn 11113 ax-1cn 11114 ax-icn 11115 ax-addcl 11116 ax-addrcl 11117 ax-mulcl 11118 ax-mulrcl 11119 ax-mulcom 11120 ax-addass 11121 ax-mulass 11122 ax-distr 11123 ax-i2m1 11124 ax-1ne0 11125 ax-1rid 11126 ax-rnegex 11127 ax-rrecex 11128 ax-cnre 11129 ax-pre-lttri 11130 ax-pre-lttrn 11131 ax-pre-ltadd 11132 ax-pre-mulgt0 11133 ax-pre-sup 11134 ax-addf 11135 ax-mulf 11136 |
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 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-rmo 3352 df-reu 3353 df-rab 3407 df-v 3446 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-pss 3930 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-tp 4592 df-op 4594 df-uni 4867 df-int 4909 df-iun 4957 df-iin 4958 df-br 5107 df-opab 5169 df-mpt 5190 df-tr 5224 df-id 5532 df-eprel 5538 df-po 5546 df-so 5547 df-fr 5589 df-se 5590 df-we 5591 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-pred 6254 df-ord 6321 df-on 6322 df-lim 6323 df-suc 6324 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-isom 6506 df-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 df-of 7618 df-om 7804 df-1st 7922 df-2nd 7923 df-supp 8094 df-frecs 8213 df-wrecs 8244 df-recs 8318 df-rdg 8357 df-1o 8413 df-2o 8414 df-er 8651 df-map 8770 df-pm 8771 df-ixp 8839 df-en 8887 df-dom 8888 df-sdom 8889 df-fin 8890 df-fsupp 9309 df-fi 9352 df-sup 9383 df-inf 9384 df-oi 9451 df-card 9880 df-pnf 11196 df-mnf 11197 df-xr 11198 df-ltxr 11199 df-le 11200 df-sub 11392 df-neg 11393 df-div 11818 df-nn 12159 df-2 12221
df-3 12222 df-4 12223
df-5 12224 df-6 12225
df-7 12226 df-8 12227
df-9 12228 df-n0 12419 df-z 12505
df-dec 12624 df-uz 12769 df-q 12879
df-rp 12921 df-xneg 13038 df-xadd 13039 df-xmul 13040 df-ioo 13274 df-ioc 13275 df-ico 13276 df-icc 13277 df-fz 13431 df-fzo 13574 df-fl 13703 df-mod 13781 df-seq 13913 df-exp 13974 df-fac 14180 df-bc 14209 df-hash 14237 df-shft 14958 df-cj 14990 df-re 14991 df-im 14992 df-sqrt 15126 df-abs 15127 df-limsup 15359 df-clim 15376 df-rlim 15377 df-sum 15577 df-ef 15955 df-sin 15957 df-cos 15958 df-pi 15960 df-struct 17024 df-sets 17041 df-slot 17059 df-ndx 17071 df-base 17089 df-ress 17118 df-plusg 17151 df-mulr 17152 df-starv 17153 df-sca 17154 df-vsca 17155 df-ip 17156 df-tset 17157 df-ple 17158 df-ds 17160 df-unif 17161 df-hom 17162 df-cco 17163 df-rest 17309 df-topn 17310 df-0g 17328 df-gsum 17329 df-topgen 17330 df-pt 17331 df-prds 17334 df-xrs 17389 df-qtop 17394 df-imas 17395 df-xps 17397 df-mre 17471 df-mrc 17472 df-acs 17474 df-mgm 18502 df-sgrp 18551 df-mnd 18562 df-submnd 18607 df-mulg 18878 df-cntz 19102 df-cmn 19569 df-psmet 20804 df-xmet 20805 df-met 20806 df-bl 20807 df-mopn 20808 df-fbas 20809 df-fg 20810 df-cnfld 20813 df-top 22259 df-topon 22276 df-topsp 22298 df-bases 22312 df-cld 22386 df-ntr 22387 df-cls 22388 df-nei 22465 df-lp 22503 df-perf 22504 df-cn 22594 df-cnp 22595 df-haus 22682 df-tx 22929 df-hmeo 23122 df-fil 23213 df-fm 23305 df-flim 23306 df-flf 23307 df-xms 23689 df-ms 23690 df-tms 23691 df-cncf 24257 df-limc 25246 df-dv 25247 df-log 25928 |
This theorem is referenced by: logcnlem3
26015 advlogexp
26026 logccv
26034 recxpcl
26046 cxpsqrt
26074 loglesqrt
26127 logbrec
26148 logbleb
26149 logblt
26150 ang180lem2
26176 isosctrlem2
26185 atanlogaddlem
26279 atantan
26289 birthdaylem2
26318 birthdaylem3
26319 amgmlem
26355 emcllem1
26361 emcllem2
26362 emcllem3
26363 emcllem4
26364 emcllem5
26365 emcllem6
26366 harmonicubnd
26375 fsumharmonic
26377 zetacvg
26380 lgamgulmlem3
26396 lgamgulmlem4
26397 lgamgulmlem5
26398 lgamgulmlem6
26399 lgamgulm2
26401 lgambdd
26402 lgamcvg2
26420 gamcvg
26421 gamcvg2lem
26424 relgamcl
26427 lgam1
26429 chtf
26473 efchtcl
26476 chtge0
26477 vmacl
26483 chtprm
26518 chtdif
26523 efchtdvds
26524 prmorcht
26543 vmalelog
26569 chtleppi
26574 chtublem
26575 fsumvma2
26578 pclogsum
26579 vmasum
26580 chpval2
26582 chpchtsum
26583 chpub
26584 logfacubnd
26585 logfaclbnd
26586 logexprlim
26589 logfacrlim2
26590 bposlem1
26648 bposlem9
26656 chebbnd1lem1
26833 chebbnd1lem2
26834 chebbnd1lem3
26835 chtppilimlem1
26837 chpchtlim
26843 vmadivsum
26846 vmadivsumb
26847 rplogsumlem1
26848 rplogsumlem2
26849 rpvmasumlem
26851 dchrvmasumlem1
26859 dchrvmasum2lem
26860 dchrvmasum2if
26861 dchrvmasumlem2
26862 dchrvmasumiflem1
26865 dchrvmasumiflem2
26866 rplogsum
26891 mulogsumlem
26895 mulogsum
26896 mulog2sumlem1
26898 mulog2sumlem2
26899 mulog2sumlem3
26900 vmalogdivsum2
26902 vmalogdivsum
26903 2vmadivsumlem
26904 logsqvma
26906 logsqvma2
26907 log2sumbnd
26908 selberglem2
26910 selbergb
26913 selberg2lem
26914 selberg2b
26916 chpdifbndlem1
26917 chpdifbndlem2
26918 logdivbnd
26920 selberg3lem1
26921 selberg3lem2
26922 selberg3
26923 selberg4lem1
26924 selberg4
26925 selberg3r
26933 selberg4r
26934 selberg34r
26935 pntsf
26937 pntsval2
26940 pntrlog2bndlem1
26941 pntrlog2bndlem2
26942 pntrlog2bndlem3
26943 pntrlog2bndlem4
26944 pntrlog2bndlem5
26945 pntrlog2bndlem6
26947 pntrlog2bnd
26948 pntpbnd1a
26949 pntpbnd2
26951 pntibndlem2
26955 pntlemb
26961 pntlemg
26962 pntlemh
26963 pntlemn
26964 pntlemr
26966 pntlemj
26967 pntlemf
26969 pntlemk
26970 pntlemo
26971 ostth2lem4
27000 ostth2
27001 ostth3
27002 xrge0iifcnv
32571 xrge0iifiso
32573 xrge0iifhom
32575 hgt750lemd
33318 logdivsqrle
33320 hgt750lem
33321 hgt750lemb
33326 hgt750leme
33328 tgoldbachgtde
33330 dvrelogpow2b
40571 aks4d1p1p6
40576 aks4d1p1p7
40577 aks4d1p1p5
40578 aks4d1p6
40584 stirlinglem4
44404 stirlinglem11
44411 stirlinglem12
44412 stirlinglem13
44413 lighneallem2
45884 rege1logbrege0
46730 amgmwlem
47335 |