Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1540
∈ wcel 2105 dom cdm 5620
‘cfv 6479 (class class class)co 7337
Fincfn 8804 0cc0 10972
+∞cpnf 11107 [,]cicc 13183
volncvoln 44422 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912
ax-6 1970 ax-7 2010 ax-8 2107
ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2707 ax-rep 5229 ax-sep 5243 ax-nul 5250 ax-pow 5308 ax-pr 5372 ax-un 7650 ax-inf2 9498 ax-cc 10292 ax-ac2 10320 ax-cnex 11028 ax-resscn 11029 ax-1cn 11030 ax-icn 11031 ax-addcl 11032 ax-addrcl 11033 ax-mulcl 11034 ax-mulrcl 11035 ax-mulcom 11036 ax-addass 11037 ax-mulass 11038 ax-distr 11039 ax-i2m1 11040 ax-1ne0 11041 ax-1rid 11042 ax-rnegex 11043 ax-rrecex 11044 ax-cnre 11045 ax-pre-lttri 11046 ax-pre-lttrn 11047 ax-pre-ltadd 11048 ax-pre-mulgt0 11049 ax-pre-sup 11050 ax-addf 11051 ax-mulf 11052 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2538 df-eu 2567 df-clab 2714 df-cleq 2728 df-clel 2814 df-nfc 2886 df-ne 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-rmo 3349 df-reu 3350 df-rab 3404 df-v 3443 df-sbc 3728 df-csb 3844 df-dif 3901 df-un 3903 df-in 3905 df-ss 3915 df-pss 3917 df-nul 4270 df-if 4474 df-pw 4549 df-sn 4574 df-pr 4576 df-tp 4578 df-op 4580 df-uni 4853 df-int 4895 df-iun 4943 df-disj 5058 df-br 5093 df-opab 5155 df-mpt 5176 df-tr 5210 df-id 5518 df-eprel 5524 df-po 5532 df-so 5533 df-fr 5575 df-se 5576 df-we 5577 df-xp 5626 df-rel 5627 df-cnv 5628 df-co 5629 df-dm 5630 df-rn 5631 df-res 5632 df-ima 5633 df-pred 6238 df-ord 6305 df-on 6306 df-lim 6307 df-suc 6308 df-iota 6431 df-fun 6481 df-fn 6482 df-f 6483 df-f1 6484 df-fo 6485 df-f1o 6486 df-fv 6487 df-isom 6488 df-riota 7293 df-ov 7340 df-oprab 7341 df-mpo 7342 df-of 7595 df-om 7781 df-1st 7899 df-2nd 7900 df-tpos 8112 df-frecs 8167 df-wrecs 8198 df-recs 8272 df-rdg 8311 df-1o 8367 df-2o 8368 df-oadd 8371 df-omul 8372 df-er 8569 df-map 8688 df-pm 8689 df-ixp 8757 df-en 8805 df-dom 8806 df-sdom 8807 df-fin 8808 df-fi 9268 df-sup 9299 df-inf 9300 df-oi 9367 df-dju 9758 df-card 9796 df-acn 9799 df-ac 9973 df-pnf 11112 df-mnf 11113 df-xr 11114 df-ltxr 11115 df-le 11116 df-sub 11308 df-neg 11309 df-div 11734 df-nn 12075 df-2 12137
df-3 12138 df-4 12139
df-5 12140 df-6 12141
df-7 12142 df-8 12143
df-9 12144 df-n0 12335 df-z 12421
df-dec 12539 df-uz 12684 df-q 12790
df-rp 12832 df-xneg 12949 df-xadd 12950 df-xmul 12951 df-ioo 13184 df-ico 13186 df-icc 13187 df-fz 13341 df-fzo 13484 df-fl 13613 df-seq 13823 df-exp 13884 df-hash 14146 df-cj 14909 df-re 14910 df-im 14911 df-sqrt 15045 df-abs 15046 df-clim 15296 df-rlim 15297 df-sum 15497 df-prod 15715 df-struct 16945 df-sets 16962 df-slot 16980 df-ndx 16992 df-base 17010 df-ress 17039 df-plusg 17072 df-mulr 17073 df-starv 17074 df-tset 17078 df-ple 17079 df-ds 17081 df-unif 17082 df-rest 17230 df-0g 17249 df-topgen 17251 df-mgm 18423 df-sgrp 18472 df-mnd 18483 df-grp 18676 df-minusg 18677 df-subg 18848 df-cmn 19483 df-abl 19484 df-mgp 19816 df-ur 19833 df-ring 19880 df-cring 19881 df-oppr 19957 df-dvdsr 19978 df-unit 19979 df-invr 20009 df-dvr 20020 df-drng 20095 df-psmet 20695 df-xmet 20696 df-met 20697 df-bl 20698 df-mopn 20699 df-cnfld 20704 df-top 22149 df-topon 22166 df-bases 22202 df-cmp 22644 df-ovol 24734 df-vol 24735 df-salg 44195 df-sumge0 44247 df-mea 44334 df-ome 44374 df-caragen 44376 df-ovoln 44421 df-voln 44423 |
This theorem is referenced by: vonxrcl
44552 |