Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2104
⊆ wss 3947 Or wor 5586
supcsup 9437 ℝ*cxr 11251 <
clt 11252 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911
ax-6 1969 ax-7 2009 ax-8 2106
ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5298 ax-nul 5305 ax-pow 5362 ax-pr 5426 ax-un 7727 ax-cnex 11168 ax-resscn 11169 ax-1cn 11170 ax-icn 11171 ax-addcl 11172 ax-addrcl 11173 ax-mulcl 11174 ax-mulrcl 11175 ax-mulcom 11176 ax-addass 11177 ax-mulass 11178 ax-distr 11179 ax-i2m1 11180 ax-1ne0 11181 ax-1rid 11182 ax-rnegex 11183 ax-rrecex 11184 ax-cnre 11185 ax-pre-lttri 11186 ax-pre-lttrn 11187 ax-pre-ltadd 11188 ax-pre-mulgt0 11189 ax-pre-sup 11190 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 844 df-3or 1086 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-ne 2939 df-nel 3045 df-ral 3060 df-rex 3069 df-rmo 3374 df-reu 3375 df-rab 3431 df-v 3474 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4322 df-if 4528 df-pw 4603 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-br 5148 df-opab 5210 df-mpt 5231 df-id 5573 df-po 5587 df-so 5588 df-xp 5681 df-rel 5682 df-cnv 5683 df-co 5684 df-dm 5685 df-rn 5686 df-res 5687 df-ima 5688 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-f1 6547 df-fo 6548 df-f1o 6549 df-fv 6550 df-riota 7367 df-ov 7414 df-oprab 7415 df-mpo 7416 df-er 8705 df-en 8942 df-dom 8943 df-sdom 8944 df-sup 9439 df-pnf 11254 df-mnf 11255 df-xr 11256 df-ltxr 11257 df-le 11258 df-sub 11450 df-neg 11451 |
This theorem is referenced by: supxrun
13299 supxrmnf
13300 supxrbnd1
13304 supxrbnd2
13305 supxrub
13307 supxrleub
13309 supxrre
13310 supxrbnd
13311 supxrgtmnf
13312 supxrre1
13313 supxrre2
13314 supxrss
13315 ixxub
13349 limsupgord
15420 limsupcl
15421 limsupgf
15423 prdsdsf
24093 xpsdsval
24107 xrge0tsms
24570 elovolm
25224 ovolmge0
25226 ovolgelb
25229 ovollb2lem
25237 ovolunlem1a
25245 ovoliunlem1
25251 ovoliunlem2
25252 ovoliun
25254 ovolscalem1
25262 ovolicc1
25265 ovolicc2lem4
25269 voliunlem2
25300 voliunlem3
25301 ioombl1lem2
25308 uniioovol
25328 uniiccvol
25329 uniioombllem1
25330 uniioombllem3
25334 itg2cl
25482 itg2seq
25492 itg2monolem2
25501 itg2monolem3
25502 itg2mono
25503 mdeglt
25818 mdegxrcl
25820 radcnvcl
26165 nmoxr
30286 nmopxr
31386 nmfnxr
31399 xrofsup
32247 supxrnemnf
32248 xrge0tsmsd
32479 mblfinlem3
36830 mblfinlem4
36831 ismblfin
36832 itg2addnclem
36842 itg2gt0cn
36846 binomcxplemdvbinom
43414 binomcxplemcvg
43415 binomcxplemnotnn0
43417 supxrcld
44097 supxrgere
44341 supxrgelem
44345 supxrge
44346 suplesup
44347 suplesup2
44384 supxrcli
44442 liminfval2
44782 liminflelimsuplem
44789 sge0cl
45395 sge0xaddlem1
45447 sge0xaddlem2
45448 sge0reuz
45461 |