Colors of
variables: wff
setvar class |
Syntax hints:
∈ wcel 2107 class class class wbr 5104
(class class class)co 7350 0cc0 10985
+∞cpnf 11120 ℝ*cxr 11122 ≤
cle 11124 [,]cicc 13196 |
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 2709 ax-sep 5255 ax-nul 5262 ax-pow 5319 ax-pr 5383 ax-un 7663 ax-cnex 11041 ax-resscn 11042 ax-1cn 11043 ax-addrcl 11046 ax-rnegex 11056 ax-cnre 11058 ax-pre-lttri 11059 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2540 df-eu 2569 df-clab 2716 df-cleq 2730 df-clel 2816 df-nfc 2888 df-ne 2943 df-nel 3049 df-ral 3064 df-rex 3073 df-rab 3407 df-v 3446 df-sbc 3739 df-csb 3855 df-dif 3912 df-un 3914 df-in 3916 df-ss 3926 df-nul 4282 df-if 4486 df-pw 4561 df-sn 4586 df-pr 4588 df-op 4592 df-uni 4865 df-br 5105 df-opab 5167 df-mpt 5188 df-id 5529 df-xp 5637 df-rel 5638 df-cnv 5639 df-co 5640 df-dm 5641 df-rn 5642 df-res 5643 df-ima 5644 df-iota 6444 df-fun 6494 df-fn 6495 df-f 6496 df-f1 6497 df-fo 6498 df-f1o 6499 df-fv 6500 df-ov 7353 df-oprab 7354 df-mpo 7355 df-er 8582 df-en 8818 df-dom 8819 df-sdom 8820 df-pnf 11125 df-mnf 11126 df-xr 11127 df-ltxr 11128 df-le 11129 df-icc 13200 |
This theorem is referenced by: xrge0subm
20761 itg2const2
25028 itg2splitlem
25035 itg2split
25036 itg2gt0
25047 itg2cnlem2
25049 itg2cn
25050 iblss
25091 itgle
25096 itgeqa
25100 ibladdlem
25106 iblabs
25115 iblabsr
25116 iblmulc2
25117 bddmulibl
25125 bddiblnc
25128 xrge0infss
31447 xrge00
31659 unitssxrge0
32242 xrge0mulc1cn
32283 esum0
32409 esumpad
32415 esumpad2
32416 esumrnmpt2
32428 esumpinfval
32433 esummulc1
32441 ddemeas
32596 oms0
32658 itg2gt0cn
36019 ibladdnclem
36020 iblabsnc
36028 iblmulc2nc
36029 ftc1anclem7
36043 ftc1anclem8
36044 ftc1anc
36045 iblsplit
43929 gsumge0cl
44334 sge0cl
44344 sge0ss
44375 0ome
44492 ovnf
44526 |