Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2107
⊆ wss 3915 Or wor 5549
supcsup 9383 ℝ*cxr 11195 <
clt 11196 |
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 5261 ax-nul 5268 ax-pow 5325 ax-pr 5389 ax-un 7677 ax-cnex 11114 ax-resscn 11115 ax-1cn 11116 ax-icn 11117 ax-addcl 11118 ax-addrcl 11119 ax-mulcl 11120 ax-mulrcl 11121 ax-mulcom 11122 ax-addass 11123 ax-mulass 11124 ax-distr 11125 ax-i2m1 11126 ax-1ne0 11127 ax-1rid 11128 ax-rnegex 11129 ax-rrecex 11130 ax-cnre 11131 ax-pre-lttri 11132 ax-pre-lttrn 11133 ax-pre-ltadd 11134 ax-pre-mulgt0 11135 ax-pre-sup 11136 |
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 3356 df-reu 3357 df-rab 3411 df-v 3450 df-sbc 3745 df-csb 3861 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-nul 4288 df-if 4492 df-pw 4567 df-sn 4592 df-pr 4594 df-op 4598 df-uni 4871 df-br 5111 df-opab 5173 df-mpt 5194 df-id 5536 df-po 5550 df-so 5551 df-xp 5644 df-rel 5645 df-cnv 5646 df-co 5647 df-dm 5648 df-rn 5649 df-res 5650 df-ima 5651 df-iota 6453 df-fun 6503 df-fn 6504 df-f 6505 df-f1 6506 df-fo 6507 df-f1o 6508 df-fv 6509 df-riota 7318 df-ov 7365 df-oprab 7366 df-mpo 7367 df-er 8655 df-en 8891 df-dom 8892 df-sdom 8893 df-sup 9385 df-pnf 11198 df-mnf 11199 df-xr 11200 df-ltxr 11201 df-le 11202 df-sub 11394 df-neg 11395 |
This theorem is referenced by: supxrun
13242 supxrmnf
13243 supxrbnd1
13247 supxrbnd2
13248 supxrub
13250 supxrleub
13252 supxrre
13253 supxrbnd
13254 supxrgtmnf
13255 supxrre1
13256 supxrre2
13257 supxrss
13258 ixxub
13292 limsupgord
15361 limsupcl
15362 limsupgf
15364 prdsdsf
23736 xpsdsval
23750 xrge0tsms
24213 elovolm
24855 ovolmge0
24857 ovolgelb
24860 ovollb2lem
24868 ovolunlem1a
24876 ovoliunlem1
24882 ovoliunlem2
24883 ovoliun
24885 ovolscalem1
24893 ovolicc1
24896 ovolicc2lem4
24900 voliunlem2
24931 voliunlem3
24932 ioombl1lem2
24939 uniioovol
24959 uniiccvol
24960 uniioombllem1
24961 uniioombllem3
24965 itg2cl
25113 itg2seq
25123 itg2monolem2
25132 itg2monolem3
25133 itg2mono
25134 mdeglt
25446 mdegxrcl
25448 radcnvcl
25792 nmoxr
29750 nmopxr
30850 nmfnxr
30863 xrofsup
31714 supxrnemnf
31715 xrge0tsmsd
31941 mblfinlem3
36146 mblfinlem4
36147 ismblfin
36148 itg2addnclem
36158 itg2gt0cn
36162 binomcxplemdvbinom
42707 binomcxplemcvg
42708 binomcxplemnotnn0
42710 supxrcld
43391 supxrgere
43641 supxrgelem
43645 supxrge
43646 suplesup
43647 suplesup2
43684 supxrcli
43743 liminfval2
44083 liminflelimsuplem
44090 sge0cl
44696 sge0xaddlem1
44748 sge0xaddlem2
44749 sge0reuz
44762 |