| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∈ wcel 2106
class class class wbr 5140 (class class class)co 7392
ℝcr 11090 0cc0 11091
≤ cle 11230 ↑𝑐ccxp 25990 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2702 ax-rep 5277 ax-sep 5291 ax-nul 5298 ax-pow 5355 ax-pr 5419 ax-un 7707 ax-inf2 9617 ax-cnex 11147 ax-resscn 11148 ax-1cn 11149 ax-icn 11150 ax-addcl 11151 ax-addrcl 11152 ax-mulcl 11153 ax-mulrcl 11154 ax-mulcom 11155 ax-addass 11156 ax-mulass 11157 ax-distr 11158 ax-i2m1 11159 ax-1ne0 11160 ax-1rid 11161 ax-rnegex 11162 ax-rrecex 11163 ax-cnre 11164 ax-pre-lttri 11165 ax-pre-lttrn 11166 ax-pre-ltadd 11167 ax-pre-mulgt0 11168 ax-pre-sup 11169 ax-addf 11170 ax-mulf 11171 |
| This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3or 1088 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-nel 3046 df-ral 3061 df-rex 3070 df-rmo 3375 df-reu 3376 df-rab 3432 df-v 3474 df-sbc 3773 df-csb 3889 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-pss 3962 df-nul 4318 df-if 4522 df-pw 4597 df-sn 4622 df-pr 4624 df-tp 4626 df-op 4628 df-uni 4901 df-int 4943 df-iun 4991 df-iin 4992 df-br 5141 df-opab 5203 df-mpt 5224 df-tr 5258 df-id 5566 df-eprel 5572 df-po 5580 df-so 5581 df-fr 5623 df-se 5624 df-we 5625 df-xp 5674 df-rel 5675 df-cnv 5676 df-co 5677 df-dm 5678 df-rn 5679 df-res 5680 df-ima 5681 df-pred 6288 df-ord 6355 df-on 6356 df-lim 6357 df-suc 6358 df-iota 6483 df-fun 6533 df-fn 6534 df-f 6535 df-f1 6536 df-fo 6537 df-f1o 6538 df-fv 6539 df-isom 6540 df-riota 7348 df-ov 7395 df-oprab 7396 df-mpo 7397 df-of 7652 df-om 7838 df-1st 7956 df-2nd 7957 df-supp 8128 df-frecs 8247 df-wrecs 8278 df-recs 8352 df-rdg 8391 df-1o 8447 df-2o 8448 df-er 8685 df-map 8804 df-pm 8805 df-ixp 8874 df-en 8922 df-dom 8923 df-sdom 8924 df-fin 8925 df-fsupp 9344 df-fi 9387 df-sup 9418 df-inf 9419 df-oi 9486 df-card 9915 df-pnf 11231 df-mnf 11232 df-xr 11233 df-ltxr 11234 df-le 11235 df-sub 11427 df-neg 11428 df-div 11853 df-nn 12194 df-2 12256
df-3 12257 df-4 12258
df-5 12259 df-6 12260
df-7 12261 df-8 12262
df-9 12263 df-n0 12454 df-z 12540
df-dec 12659 df-uz 12804 df-q 12914
df-rp 12956 df-xneg 13073 df-xadd 13074 df-xmul 13075 df-ioo 13309 df-ioc 13310 df-ico 13311 df-icc 13312 df-fz 13466 df-fzo 13609 df-fl 13738 df-mod 13816 df-seq 13948 df-exp 14009 df-fac 14215 df-bc 14244 df-hash 14272 df-shft 14995 df-cj 15027 df-re 15028 df-im 15029 df-sqrt 15163 df-abs 15164 df-limsup 15396 df-clim 15413 df-rlim 15414 df-sum 15614 df-ef 15992 df-sin 15994 df-cos 15995 df-pi 15997 df-struct 17061 df-sets 17078 df-slot 17096 df-ndx 17108 df-base 17126 df-ress 17155 df-plusg 17191 df-mulr 17192 df-starv 17193 df-sca 17194 df-vsca 17195 df-ip 17196 df-tset 17197 df-ple 17198 df-ds 17200 df-unif 17201 df-hom 17202 df-cco 17203 df-rest 17349 df-topn 17350 df-0g 17368 df-gsum 17369 df-topgen 17370 df-pt 17371 df-prds 17374 df-xrs 17429 df-qtop 17434 df-imas 17435 df-xps 17437 df-mre 17511 df-mrc 17512 df-acs 17514 df-mgm 18542 df-sgrp 18591 df-mnd 18602 df-submnd 18647 df-mulg 18922 df-cntz 19146 df-cmn 19613 df-psmet 20867 df-xmet 20868 df-met 20869 df-bl 20870 df-mopn 20871 df-fbas 20872 df-fg 20873 df-cnfld 20876 df-top 22322 df-topon 22339 df-topsp 22361 df-bases 22375 df-cld 22449 df-ntr 22450 df-cls 22451 df-nei 22528 df-lp 22566 df-perf 22567 df-cn 22657 df-cnp 22658 df-haus 22745 df-tx 22992 df-hmeo 23185 df-fil 23276 df-fm 23368 df-flim 23369 df-flf 23370 df-xms 23752 df-ms 23753 df-tms 23754 df-cncf 24320 df-limc 25309 df-dv 25310 df-log 25991 df-cxp 25992 |
| This theorem is referenced by: cxpaddlelem
26183 cxpaddle
26184 abscxpbnd
26185 chpchtsum
26646 etransclem23
44734 |
