Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1542
∈ wcel 2107 ∀wral 3065 ∖ cdif 3908
∩ cin 3910 ⊆
wss 3911 𝒫 cpw 4561
dom cdm 5634 ‘cfv 6497
(class class class)co 7358 ℝcr 11051
+ caddc 11055 vol*covol 24829 volcvol 24830 |
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 2708 ax-sep 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-cnex 11108 ax-resscn 11109 ax-1cn 11110 ax-icn 11111 ax-addcl 11112 ax-addrcl 11113 ax-mulcl 11114 ax-mulrcl 11115 ax-mulcom 11116 ax-addass 11117 ax-mulass 11118 ax-distr 11119 ax-i2m1 11120 ax-1ne0 11121 ax-1rid 11122 ax-rnegex 11123 ax-rrecex 11124 ax-cnre 11125 ax-pre-lttri 11126 ax-pre-lttrn 11127 ax-pre-ltadd 11128 ax-pre-mulgt0 11129 ax-pre-sup 11130 |
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 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ne 2945 df-nel 3051 df-ral 3066 df-rex 3075 df-rmo 3354 df-reu 3355 df-rab 3409 df-v 3448 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-op 4594 df-uni 4867 df-iun 4957 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-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-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 df-om 7804 df-1st 7922 df-2nd 7923 df-frecs 8213 df-wrecs 8244 df-recs 8318 df-rdg 8357 df-er 8649 df-map 8768 df-en 8885 df-dom 8886 df-sdom 8887 df-sup 9379 df-inf 9380 df-pnf 11192 df-mnf 11193 df-xr 11194 df-ltxr 11195 df-le 11196 df-sub 11388 df-neg 11389 df-div 11814 df-nn 12155 df-2 12217
df-3 12218 df-n0 12415 df-z 12501
df-uz 12765 df-rp 12917 df-ico 13271 df-icc 13272 df-fz 13426 df-seq 13908 df-exp 13969 df-cj 14985 df-re 14986 df-im 14987 df-sqrt 15121 df-abs 15122 df-ovol 24831 df-vol 24832 |
This theorem is referenced by: volss
24900 nulmbl2
24903 unmbl
24904 shftmbl
24905 unidmvol
24908 inmbl
24909 difmbl
24910 volun
24912 volinun
24913 volfiniun
24914 voliunlem2
24918 voliunlem3
24919 volsup
24923 volsup2
24972 volcn
24973 vitalilem4
24978 vitalilem5
24979 vitali
24980 ismbf
24995 ismbfcn
24996 mbfconst
25000 mbfid
25002 cncombf
25025 cnmbf
25026 i1fima2
25046 i1fd
25048 itg1ge0
25053 i1f1lem
25056 itg11
25058 i1fadd
25062 i1fmul
25063 itg1addlem2
25064 itg1addlem5
25068 i1fres
25073 itg1ge0a
25079 itg1climres
25082 mbfi1fseqlem4
25086 mbfi1flim
25091 mbfmullem2
25092 itg2const2
25109 itg2splitlem
25116 itg2split
25117 itg2gt0
25128 itg2cnlem2
25130 ibladdlem
25187 itgaddlem1
25190 iblabslem
25195 itggt0
25211 itgcn
25212 ftc1lem4
25406 itgulm
25770 areaf
26314 dmvlsiga
32731 volsupnfl
36126 cnambfre
36129 itg2addnclem
36132 ibladdnclem
36137 itgaddnclem1
36139 iblabsnclem
36144 ftc1cnnclem
36152 volge0
44209 dmvolss
44233 vonvol
44910 |