Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ wa 397
∈ wcel 2107 ⊆
wss 3911 class class class wbr 5106
(class class class)co 7358 ℝ*cxr 11189 <
clt 11190 ≤ cle 11191
(,)cioo 13265 |
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-pre-lttri 11126 ax-pre-lttrn 11127 |
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-rab 3409 df-v 3448 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 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-id 5532 df-po 5546 df-so 5547 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-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-ov 7361 df-oprab 7362 df-mpo 7363 df-1st 7922 df-2nd 7923 df-er 8649 df-en 8885 df-dom 8886 df-sdom 8887 df-pnf 11192 df-mnf 11193 df-xr 11194 df-ltxr 11195 df-le 11196 df-ioo 13269 |
This theorem is referenced by: tgqioo
24166 ioorcl2
24939 itgsplitioo
25205 ditgcl
25225 ditgswap
25226 ditgsplitlem
25227 dvferm2lem
25353 dvferm
25355 dvlip
25360 dvgt0lem1
25369 dvivthlem1
25375 lhop1lem
25380 lhop1
25381 dvcvx
25387 dvfsumle
25388 dvfsumge
25389 dvfsumabs
25390 ftc1lem1
25402 ftc1lem2
25403 ftc1a
25404 ftc1lem4
25406 ftc2
25411 ftc2ditglem
25412 itgsubstlem
25415 cos0pilt1
25891 ftc1anc
36162 ftc2nc
36163 limcresioolb
43891 fourierdlem46
44400 fourierdlem48
44402 fourierdlem49
44403 fourierdlem75
44429 fourierdlem103
44457 fourierdlem113
44467 fouriersw
44479 |