| Colors of
variables: wff
setvar class |
Syntax hints: ->wi 4 /\wa 369
=wceq 1395 e.wcel 1818 class class class wbr 4452
`cfv 5593 (class class class)co 6296
cc 9511 cr 9512 0cc0 9513 cmul 9518 cle 9650 2c2 10610 cexp 12166 ccj 12929 csqrt 13066 cabs 13067 |
| This theorem is referenced by: abs1
13130 absnid
13131 leabs
13132 absor
13133 sqabs
13140 max0add
13143 absidm
13156 abssubge0
13160 fzomaxdiflem
13175 absidi
13210 absidd
13254 o1fsum
13627 geo2lim
13684 geoihalfsum
13691 ege2le3
13825 eirrlem
13937 rpnnen2lem3
13950 rpnnen2lem9
13956 iscmet3lem3
21729 minveclem2
21841 mbfi1fseqlem6
22127 dvfsumrlim
22432 aaliou3lem3
22740 pserulm
22817 pige3
22910 efif1olem4
22932 cxpcn3lem
23121 log2cnv
23275 log2tlbnd
23276 cxplim
23301 cxploglim2
23308 divsqrtsumo1
23313 fsumharmonic
23341 logfacrlim
23499 logexprlim
23500 dchrmusum2
23679 dchrvmasumlem3
23684 dchrisum0lem1
23701 dchrisum0lem2a
23702 dchrisum0lem2
23703 mudivsum
23715 mulogsumlem
23716 log2sumbnd
23729 selberglem2
23731 selberg3lem1
23742 pntpbnd2
23772 pntibndlem2
23776 pntlemn
23785 pntlemj
23788 pntlemo
23792 nvsge0
25566 nmoub2i
25689 minvecolem2
25791 zetacvg
28557 subfacval3
28633 ftc1anclem5
30094 oddcomabszz
30880 fourierdlem68
31957 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704
ax-6 1747 ax-7 1790 ax-8 1820
ax-9 1822 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 ax-sep 4573 ax-nul 4581 ax-pow 4630 ax-pr 4691 ax-un 6592 ax-cnex 9569 ax-resscn 9570 ax-1cn 9571 ax-icn 9572 ax-addcl 9573 ax-addrcl 9574 ax-mulcl 9575 ax-mulrcl 9576 ax-mulcom 9577 ax-addass 9578 ax-mulass 9579 ax-distr 9580 ax-i2m1 9581 ax-1ne0 9582 ax-1rid 9583 ax-rnegex 9584 ax-rrecex 9585 ax-cnre 9586 ax-pre-lttri 9587 ax-pre-lttrn 9588 ax-pre-ltadd 9589 ax-pre-mulgt0 9590 ax-pre-sup 9591 |
| This theorem depends on definitions:
df-bi 185 df-or 370
df-an 371 df-3or 974 df-3an 975 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-eu 2286 df-mo 2287 df-clab 2443 df-cleq 2449 df-clel 2452 df-nfc 2607 df-ne 2654 df-nel 2655 df-ral 2812 df-rex 2813 df-reu 2814 df-rmo 2815 df-rab 2816 df-v 3111 df-sbc 3328 df-csb 3435 df-dif 3478 df-un 3480 df-in 3482 df-ss 3489 df-pss 3491 df-nul 3785 df-if 3942 df-pw 4014 df-sn 4030 df-pr 4032 df-tp 4034 df-op 4036 df-uni 4250 df-iun 4332 df-br 4453 df-opab 4511 df-mpt 4512 df-tr 4546 df-eprel 4796 df-id 4800 df-po 4805 df-so 4806 df-fr 4843 df-we 4845 df-ord 4886 df-on 4887 df-lim 4888 df-suc 4889 df-xp 5010 df-rel 5011 df-cnv 5012 df-co 5013 df-dm 5014 df-rn 5015 df-res 5016 df-ima 5017 df-iota 5556 df-fun 5595 df-fn 5596 df-f 5597 df-f1 5598 df-fo 5599 df-f1o 5600 df-fv 5601 df-riota 6257 df-ov 6299 df-oprab 6300 df-mpt2 6301 df-om 6701 df-2nd 6801 df-recs 7061 df-rdg 7095 df-er 7330 df-en 7537 df-dom 7538 df-sdom 7539 df-sup 7921 df-pnf 9651 df-mnf 9652 df-xr 9653 df-ltxr 9654 df-le 9655 df-sub 9830 df-neg 9831 df-div 10232 df-nn 10562 df-2 10619
df-3 10620 df-n0 10821 df-z 10890
df-uz 11111 df-rp 11250 df-seq 12108 df-exp 12167 df-cj 12932 df-re 12933 df-im 12934 df-sqrt 13068 df-abs 13069 |
