Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2104
class class class wbr 5147 (class class class)co 7411
ℝcr 11111 ≤
cle 11253 / cdiv 11875
ℝ+crp 12978 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911
ax-6 1969 ax-7 2009 ax-8 2106
ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5298 ax-nul 5305 ax-pow 5362 ax-pr 5426 ax-un 7727 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 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 844 df-3or 1086 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-ne 2939 df-nel 3045 df-ral 3060 df-rex 3069 df-rmo 3374 df-reu 3375 df-rab 3431 df-v 3474 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4322 df-if 4528 df-pw 4603 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-br 5148 df-opab 5210 df-mpt 5231 df-id 5573 df-po 5587 df-so 5588 df-xp 5681 df-rel 5682 df-cnv 5683 df-co 5684 df-dm 5685 df-rn 5686 df-res 5687 df-ima 5688 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-f1 6547 df-fo 6548 df-f1o 6549 df-fv 6550 df-riota 7367 df-ov 7414 df-oprab 7415 df-mpo 7416 df-er 8705 df-en 8942 df-dom 8943 df-sdom 8944 df-pnf 11254 df-mnf 11255 df-xr 11256 df-ltxr 11257 df-le 11258 df-sub 11450 df-neg 11451 df-div 11876 df-rp 12979 |
This theorem is referenced by: aalioulem5
26085 aalioulem6
26086 cxp2lim
26717 cxploglim2
26719 fsumharmonic
26752 lgamgulmlem2
26770 lgamgulmlem5
26773 chpchtlim
27218 dchrmusum2
27233 dchrvmasumlem3
27238 dchrisum0fno1
27250 dchrisum0lem1
27255 dchrisum0lem2a
27256 mulogsumlem
27270 vmalogdivsum2
27277 2vmadivsumlem
27279 selberglem2
27285 selbergb
27288 selberg2b
27291 chpdifbndlem1
27292 logdivbnd
27295 selberg3lem1
27296 selberg4lem1
27299 pntrlog2bndlem1
27316 pntrlog2bndlem2
27317 pntrlog2bndlem3
27318 pntrlog2bndlem5
27320 pntrlog2bnd
27323 pntpbnd1a
27324 pntpbnd2
27326 pntibndlem2
27330 dya2icoseg
33574 sxbrsigalem2
33583 knoppndvlem14
35704 knoppndvlem17
35707 lcmineqlem23
41222 aks4d1p1p2
41241 hashnzfzclim
43383 oddfl
44285 lefldiveq
44300 sumnnodd
44644 wallispilem5
45083 dirkertrigeqlem3
45114 fourierdlem6
45127 fourierdlem7
45128 fourierdlem10
45131 fourierdlem30
45151 fourierdlem39
45160 fourierdlem47
45167 fourierdlem65
45185 fourierdlem79
45199 etransclem23
45271 flnn0div2ge
47306 dignn0flhalflem2
47389 |