| Colors of
variables: wff
setvar class |
Syntax hints: ->wi 4 /\wa 369
e.wcel 1818 =/=wne 2652 (class class class)co 6296
cr 9512 0cc0 9513 cdiv 10231 cn 10561 |
| This theorem is referenced by: nnrecre
10597 nndivred
10609 fldiv2
11988 zmodcl
12015 iexpcyc
12272 sqrlem7
13082 expcnv
13675 ef01bndlem
13919 sin01bnd
13920 cos01bnd
13921 rpnnen2lem2
13949 rpnnen2lem3
13950 rpnnen2lem4
13951 rpnnen2lem9
13956 fldivp1
14416 ovoliunlem1
21913 dyadf
22000 dyadovol
22002 mbfi1fseqlem3
22124 mbfi1fseqlem4
22125 dveflem
22380 plyeq0lem
22607 tangtx
22898 tan4thpi
22907 root1id
23128 root1eq1
23129 root1cj
23130 cxpeq
23131 1cubrlem
23172 atan1
23259 log2tlbnd
23276 log2ublem1
23277 log2ublem2
23278 log2ub
23280 birthdaylem3
23283 birthday
23284 basellem5
23358 basellem8
23361 ppiub
23479 logfac2
23492 dchrptlem1
23539 dchrptlem2
23540 bposlem3
23561 bposlem4
23562 bposlem5
23563 bposlem6
23564 bposlem9
23567 vmadivsum
23667 dchrisum0lem1a
23671 dchrmusum2
23679 dchrvmasum2if
23682 dchrvmasumlem2
23683 dchrvmasumiflem1
23686 dchrvmasumiflem2
23687 dchrisum0re
23698 dchrisum0lem1b
23700 dchrisum0lem1
23701 dchrvmasumlem
23708 rplogsum
23712 mudivsum
23715 selberg2
23736 chpdifbndlem1
23738 selberg3lem1
23742 selbergr
23753 pntlemb
23782 pntlemg
23783 pntlemf
23790 snmlff
28774 sinccvglem
29038 circum
29040 |
| 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-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 |
| 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-recs 7061 df-rdg 7095 df-er 7330 df-en 7537 df-dom 7538 df-sdom 7539 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 |
