| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 = wceq 1541
∈ wcel 2106 ∀wral 3061 ∖ cdif 3944
∩ cin 3946 ⊆
wss 3947 𝒫 cpw 4601
dom cdm 5675 ‘cfv 6540
(class class class)co 7405 ℝcr 11105
+ caddc 11109 vol*covol 24970 volcvol 24971 |
| 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-sep 5298 ax-nul 5305 ax-pow 5362 ax-pr 5426 ax-un 7721 ax-cnex 11162 ax-resscn 11163 ax-1cn 11164 ax-icn 11165 ax-addcl 11166 ax-addrcl 11167 ax-mulcl 11168 ax-mulrcl 11169 ax-mulcom 11170 ax-addass 11171 ax-mulass 11172 ax-distr 11173 ax-i2m1 11174 ax-1ne0 11175 ax-1rid 11176 ax-rnegex 11177 ax-rrecex 11178 ax-cnre 11179 ax-pre-lttri 11180 ax-pre-lttrn 11181 ax-pre-ltadd 11182 ax-pre-mulgt0 11183 ax-pre-sup 11184 |
| 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 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-pss 3966 df-nul 4322 df-if 4528 df-pw 4603 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-iun 4998 df-br 5148 df-opab 5210 df-mpt 5231 df-tr 5265 df-id 5573 df-eprel 5579 df-po 5587 df-so 5588 df-fr 5630 df-we 5632 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-pred 6297 df-ord 6364 df-on 6365 df-lim 6366 df-suc 6367 df-iota 6492 df-fun 6542 df-fn 6543 df-f 6544 df-f1 6545 df-fo 6546 df-f1o 6547 df-fv 6548 df-riota 7361 df-ov 7408 df-oprab 7409 df-mpo 7410 df-om 7852 df-1st 7971 df-2nd 7972 df-frecs 8262 df-wrecs 8293 df-recs 8367 df-rdg 8406 df-er 8699 df-map 8818 df-en 8936 df-dom 8937 df-sdom 8938 df-sup 9433 df-inf 9434 df-pnf 11246 df-mnf 11247 df-xr 11248 df-ltxr 11249 df-le 11250 df-sub 11442 df-neg 11443 df-div 11868 df-nn 12209 df-2 12271
df-3 12272 df-n0 12469 df-z 12555
df-uz 12819 df-rp 12971 df-ico 13326 df-icc 13327 df-fz 13481 df-seq 13963 df-exp 14024 df-cj 15042 df-re 15043 df-im 15044 df-sqrt 15178 df-abs 15179 df-ovol 24972 df-vol 24973 |
| This theorem is referenced by: volss
25041 nulmbl2
25044 unmbl
25045 shftmbl
25046 unidmvol
25049 inmbl
25050 difmbl
25051 volun
25053 volinun
25054 volfiniun
25055 voliunlem2
25059 voliunlem3
25060 volsup
25064 volsup2
25113 volcn
25114 vitalilem4
25119 vitalilem5
25120 vitali
25121 ismbf
25136 ismbfcn
25137 mbfconst
25141 mbfid
25143 cncombf
25166 cnmbf
25167 i1fima2
25187 i1fd
25189 itg1ge0
25194 i1f1lem
25197 itg11
25199 i1fadd
25203 i1fmul
25204 itg1addlem2
25205 itg1addlem5
25209 i1fres
25214 itg1ge0a
25220 itg1climres
25223 mbfi1fseqlem4
25227 mbfi1flim
25232 mbfmullem2
25233 itg2const2
25250 itg2splitlem
25257 itg2split
25258 itg2gt0
25269 itg2cnlem2
25271 ibladdlem
25328 itgaddlem1
25331 iblabslem
25336 itggt0
25352 itgcn
25353 ftc1lem4
25547 itgulm
25911 areaf
26455 dmvlsiga
33115 volsupnfl
36521 cnambfre
36524 itg2addnclem
36527 ibladdnclem
36532 itgaddnclem1
36534 iblabsnclem
36539 ftc1cnnclem
36547 volge0
44663 dmvolss
44687 vonvol
45364 |
