Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1533
∈ wcel 2098 ∀wral 3053 ∖ cdif 3938
∩ cin 3940 ⊆
wss 3941 𝒫 cpw 4595
dom cdm 5667 ‘cfv 6534
(class class class)co 7402 ℝcr 11106
+ caddc 11110 vol*covol 25335 volcvol 25336 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2695 ax-sep 5290 ax-nul 5297 ax-pow 5354 ax-pr 5418 ax-un 7719 ax-cnex 11163 ax-resscn 11164 ax-1cn 11165 ax-icn 11166 ax-addcl 11167 ax-addrcl 11168 ax-mulcl 11169 ax-mulrcl 11170 ax-mulcom 11171 ax-addass 11172 ax-mulass 11173 ax-distr 11174 ax-i2m1 11175 ax-1ne0 11176 ax-1rid 11177 ax-rnegex 11178 ax-rrecex 11179 ax-cnre 11180 ax-pre-lttri 11181 ax-pre-lttrn 11182 ax-pre-ltadd 11183 ax-pre-mulgt0 11184 ax-pre-sup 11185 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2526 df-eu 2555 df-clab 2702 df-cleq 2716 df-clel 2802 df-nfc 2877 df-ne 2933 df-nel 3039 df-ral 3054 df-rex 3063 df-rmo 3368 df-reu 3369 df-rab 3425 df-v 3468 df-sbc 3771 df-csb 3887 df-dif 3944 df-un 3946 df-in 3948 df-ss 3958 df-pss 3960 df-nul 4316 df-if 4522 df-pw 4597 df-sn 4622 df-pr 4624 df-op 4628 df-uni 4901 df-iun 4990 df-br 5140 df-opab 5202 df-mpt 5223 df-tr 5257 df-id 5565 df-eprel 5571 df-po 5579 df-so 5580 df-fr 5622 df-we 5624 df-xp 5673 df-rel 5674 df-cnv 5675 df-co 5676 df-dm 5677 df-rn 5678 df-res 5679 df-ima 5680 df-pred 6291 df-ord 6358 df-on 6359 df-lim 6360 df-suc 6361 df-iota 6486 df-fun 6536 df-fn 6537 df-f 6538 df-f1 6539 df-fo 6540 df-f1o 6541 df-fv 6542 df-riota 7358 df-ov 7405 df-oprab 7406 df-mpo 7407 df-om 7850 df-1st 7969 df-2nd 7970 df-frecs 8262 df-wrecs 8293 df-recs 8367 df-rdg 8406 df-er 8700 df-map 8819 df-en 8937 df-dom 8938 df-sdom 8939 df-sup 9434 df-inf 9435 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-n0 12472 df-z 12558
df-uz 12822 df-rp 12976 df-ico 13331 df-icc 13332 df-fz 13486 df-seq 13968 df-exp 14029 df-cj 15048 df-re 15049 df-im 15050 df-sqrt 15184 df-abs 15185 df-ovol 25337 df-vol 25338 |
This theorem is referenced by: volss
25406 nulmbl2
25409 unmbl
25410 shftmbl
25411 unidmvol
25414 inmbl
25415 difmbl
25416 volun
25418 volinun
25419 volfiniun
25420 voliunlem2
25424 voliunlem3
25425 volsup
25429 volsup2
25478 volcn
25479 vitalilem4
25484 vitalilem5
25485 vitali
25486 ismbf
25501 ismbfcn
25502 mbfconst
25506 mbfid
25508 cncombf
25531 cnmbf
25532 i1fima2
25552 i1fd
25554 itg1ge0
25559 i1f1lem
25562 itg11
25564 i1fadd
25568 i1fmul
25569 itg1addlem2
25570 itg1addlem5
25574 i1fres
25579 itg1ge0a
25585 itg1climres
25588 mbfi1fseqlem4
25592 mbfi1flim
25597 mbfmullem2
25598 itg2const2
25615 itg2splitlem
25622 itg2split
25623 itg2gt0
25634 itg2cnlem2
25636 ibladdlem
25693 itgaddlem1
25696 iblabslem
25701 itggt0
25717 itgcn
25718 ftc1lem4
25918 itgulm
26285 areaf
26834 dmvlsiga
33647 volsupnfl
37037 cnambfre
37040 itg2addnclem
37043 ibladdnclem
37048 itgaddnclem1
37050 iblabsnclem
37055 ftc1cnnclem
37063 volge0
45223 dmvolss
45247 vonvol
45924 |