Colors of
variables: wff
setvar class |
Syntax hints:
∈ wcel 2107 class class class wbr 5149
(class class class)co 7409 0cc0 11110
+∞cpnf 11245 ℝ*cxr 11247 ≤
cle 11249 [,]cicc 13327 |
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 2704 ax-sep 5300 ax-nul 5307 ax-pow 5364 ax-pr 5428 ax-un 7725 ax-cnex 11166 ax-resscn 11167 ax-1cn 11168 ax-addrcl 11171 ax-rnegex 11181 ax-cnre 11183 ax-pre-lttri 11184 |
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 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-nel 3048 df-ral 3063 df-rex 3072 df-rab 3434 df-v 3477 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-br 5150 df-opab 5212 df-mpt 5233 df-id 5575 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-f1 6549 df-fo 6550 df-f1o 6551 df-fv 6552 df-ov 7412 df-oprab 7413 df-mpo 7414 df-er 8703 df-en 8940 df-dom 8941 df-sdom 8942 df-pnf 11250 df-mnf 11251 df-xr 11252 df-ltxr 11253 df-le 11254 df-icc 13331 |
This theorem is referenced by: xrge0subm
20986 itg2const2
25259 itg2splitlem
25266 itg2split
25267 itg2gt0
25278 itg2cnlem2
25280 itg2cn
25281 iblss
25322 itgle
25327 itgeqa
25331 ibladdlem
25337 iblabs
25346 iblabsr
25347 iblmulc2
25348 bddmulibl
25356 bddiblnc
25359 xrge0infss
31973 xrge00
32187 unitssxrge0
32880 xrge0mulc1cn
32921 esum0
33047 esumpad
33053 esumpad2
33054 esumrnmpt2
33066 esumpinfval
33071 esummulc1
33079 ddemeas
33234 oms0
33296 itg2gt0cn
36543 ibladdnclem
36544 iblabsnc
36552 iblmulc2nc
36553 ftc1anclem7
36567 ftc1anclem8
36568 ftc1anc
36569 iblsplit
44682 gsumge0cl
45087 sge0cl
45097 sge0ss
45128 0ome
45245 ovnf
45279 |