| Colors of
variables: wff
setvar class |
Syntax hints: ->wi 4 e.wcel 1818
class class class wbr 4452 `cfv 5593
(class class class)co 6296 cr 9512 1c1 9514 caddc 9516 clt 9649 cle 9650 cfl 11927 |
| This theorem is referenced by: fracge0
11941 flge
11942 flflp1
11944 flid
11945 flwordi
11948 flval2
11950 flval3
11951 fladdz
11958 flmulnn0
11960 ceige
11972 flleceil
11980 fleqceilz
11981 quoremz
11982 quoremnn0ALT
11984 facavg
12379 rddif
13173 o1fsum
13627 flo1
13666 bitscmp
14088 prmreclem4
14437 zcld
21318 mbfi1fseqlem5
22126 mbfi1fseqlem6
22127 dvfsumlem1
22427 dvfsumlem2
22428 dvfsumlem3
22429 harmonicubnd
23339 harmonicbnd4
23340 ppisval
23377 ppiltx
23451 ppiub
23479 chtub
23487 chpub
23495 logfacubnd
23496 logfaclbnd
23497 bposlem1
23559 bposlem5
23563 bposlem6
23564 lgsquadlem1
23629 chebbnd1lem3
23656 vmadivsum
23667 dchrisumlem1
23674 dchrmusum2
23679 dchrisum0lem2a
23702 mudivsum
23715 mulogsumlem
23716 selberglem2
23731 selberg2lem
23735 pntrlog2bndlem4
23765 pntpbnd2
23772 pntlemg
23783 pntlemr
23787 pntlemk
23791 ostth2lem3
23820 ltflcei
30043 dvtanlem
30064 itg2addnclem3
30068 irrapxlem1
30758 isprm7
31192 hashnzfzclim
31227 fourierdlem4
31893 fourierdlem65
31954 |
| 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-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-nn 10562 df-n0 10821 df-z 10890
df-uz 11111 df-fl 11929 |
