| Colors of
variables: wff
setvar class |
| Syntax hints:
= wceq 1542 ∈ wcel 2107
‘cfv 6544 (class class class)co 7409
ℝcr 11109 0cc0 11110
2c2 12267 4c4 12269
(,)cioo 13324 sincsin 16007
πcpi 16010 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-rep 5286 ax-sep 5300 ax-nul 5307 ax-pow 5364 ax-pr 5428 ax-un 7725 ax-inf2 9636 ax-cnex 11166 ax-resscn 11167 ax-1cn 11168 ax-icn 11169 ax-addcl 11170 ax-addrcl 11171 ax-mulcl 11172 ax-mulrcl 11173 ax-mulcom 11174 ax-addass 11175 ax-mulass 11176 ax-distr 11177 ax-i2m1 11178 ax-1ne0 11179 ax-1rid 11180 ax-rnegex 11181 ax-rrecex 11182 ax-cnre 11183 ax-pre-lttri 11184 ax-pre-lttrn 11185 ax-pre-ltadd 11186 ax-pre-mulgt0 11187 ax-pre-sup 11188 ax-addf 11189 ax-mulf 11190 |
| This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-nel 3048 df-ral 3063 df-rex 3072 df-rmo 3377 df-reu 3378 df-rab 3434 df-v 3477 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-pss 3968 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-tp 4634 df-op 4636 df-uni 4910 df-int 4952 df-iun 5000 df-iin 5001 df-br 5150 df-opab 5212 df-mpt 5233 df-tr 5267 df-id 5575 df-eprel 5581 df-po 5589 df-so 5590 df-fr 5632 df-se 5633 df-we 5634 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-pred 6301 df-ord 6368 df-on 6369 df-lim 6370 df-suc 6371 df-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-f1 6549 df-fo 6550 df-f1o 6551 df-fv 6552 df-isom 6553 df-riota 7365 df-ov 7412 df-oprab 7413 df-mpo 7414 df-of 7670 df-om 7856 df-1st 7975 df-2nd 7976 df-supp 8147 df-frecs 8266 df-wrecs 8297 df-recs 8371 df-rdg 8410 df-1o 8466 df-2o 8467 df-er 8703 df-map 8822 df-pm 8823 df-ixp 8892 df-en 8940 df-dom 8941 df-sdom 8942 df-fin 8943 df-fsupp 9362 df-fi 9406 df-sup 9437 df-inf 9438 df-oi 9505 df-card 9934 df-pnf 11250 df-mnf 11251 df-xr 11252 df-ltxr 11253 df-le 11254 df-sub 11446 df-neg 11447 df-div 11872 df-nn 12213 df-2 12275
df-3 12276 df-4 12277
df-5 12278 df-6 12279
df-7 12280 df-8 12281
df-9 12282 df-n0 12473 df-z 12559
df-dec 12678 df-uz 12823 df-q 12933
df-rp 12975 df-xneg 13092 df-xadd 13093 df-xmul 13094 df-ioo 13328 df-ioc 13329 df-ico 13330 df-icc 13331 df-fz 13485 df-fzo 13628 df-fl 13757 df-seq 13967 df-exp 14028 df-fac 14234 df-bc 14263 df-hash 14291 df-shft 15014 df-cj 15046 df-re 15047 df-im 15048 df-sqrt 15182 df-abs 15183 df-limsup 15415 df-clim 15432 df-rlim 15433 df-sum 15633 df-ef 16011 df-sin 16013 df-cos 16014 df-pi 16016 df-struct 17080 df-sets 17097 df-slot 17115 df-ndx 17127 df-base 17145 df-ress 17174 df-plusg 17210 df-mulr 17211 df-starv 17212 df-sca 17213 df-vsca 17214 df-ip 17215 df-tset 17216 df-ple 17217 df-ds 17219 df-unif 17220 df-hom 17221 df-cco 17222 df-rest 17368 df-topn 17369 df-0g 17387 df-gsum 17388 df-topgen 17389 df-pt 17390 df-prds 17393 df-xrs 17448 df-qtop 17453 df-imas 17454 df-xps 17456 df-mre 17530 df-mrc 17531 df-acs 17533 df-mgm 18561 df-sgrp 18610 df-mnd 18626 df-submnd 18672 df-mulg 18951 df-cntz 19181 df-cmn 19650 df-psmet 20936 df-xmet 20937 df-met 20938 df-bl 20939 df-mopn 20940 df-fbas 20941 df-fg 20942 df-cnfld 20945 df-top 22396 df-topon 22413 df-topsp 22435 df-bases 22449 df-cld 22523 df-ntr 22524 df-cls 22525 df-nei 22602 df-lp 22640 df-perf 22641 df-cn 22731 df-cnp 22732 df-haus 22819 df-tx 23066 df-hmeo 23259 df-fil 23350 df-fm 23442 df-flim 23443 df-flf 23444 df-xms 23826 df-ms 23827 df-tms 23828 df-cncf 24394 df-limc 25383 df-dv 25384 |
| This theorem is referenced by: picn
25969 pipos
25970 pirp
25971 sinhalfpilem
25973 halfpire
25974 sincosq1lem
26007 sincosq2sgn
26009 sincosq3sgn
26010 sincosq4sgn
26011 coseq00topi
26012 coseq0negpitopi
26013 tangtx
26015 sinq12gt0
26017 sinq12ge0
26018 sinq34lt0t
26019 cosq14gt0
26020 cosq14ge0
26021 sincos4thpi
26023 tan4thpi
26024 sincos6thpi
26025 pigt3
26027 pige3
26028 pige3ALT
26029 coskpi
26032 sineq0
26033 coseq1
26034 cos02pilt1
26035 cosq34lt1
26036 efeq1
26037 cosne0
26038 cosordlem
26039 cosord
26040 cos0pilt1
26041 cos11
26042 sinord
26043 recosf1o
26044 resinf1o
26045 tanord1
26046 negpitopissre
26049 efif1olem1
26051 efif1olem2
26052 efif1olem4
26054 efif1o
26055 efifo
26056 eff1o
26058 ellogrn
26068 relogrn
26070 logimclad
26081 abslogimle
26082 logneg
26096 lognegb
26098 eflogeq
26110 logcj
26114 argregt0
26118 argrege0
26119 argimgt0
26120 argimlt0
26121 logimul
26122 logneg2
26123 abslogle
26126 logcnlem3
26152 dvloglem
26156 logf1o2
26158 efopnlem1
26164 efopnlem2
26165 cxpsqrtlem
26210 abscxpbnd
26261 root1eq1
26263 logreclem
26267 ang180lem1
26314 ang180lem2
26315 ang180lem3
26316 ang180lem4
26317 isosctrlem1
26323 1cubrlem
26346 asinneg
26391 asinsin
26397 asin1
26399 acosbnd
26405 atanlogaddlem
26418 atanlogsublem
26420 atanlogsub
26421 atantan
26428 atanbndlem
26430 atan1
26433 o1cxp
26479 lgamgulmlem4
26536 lgamgulmlem5
26537 lgamgulmlem6
26538 lgambdd
26541 basellem1
26585 basellem4
26588 basellem8
26592 basellem9
26593 circum
34659 logi
34704 bj-pinftyccb
36102 bj-minftyccb
36106 bj-pinftynminfty
36108 taupi
36204 sin2h
36478 cos2h
36479 tan2h
36480 acos1half
41415 proot1ex
41943 isosctrlem1ALT
43695 sineq0ALT
43698 negpilt0
43990 coseq0
44580 sinaover2ne0
44584 itgsin0pilem1
44666 itgsinexplem1
44670 itgsinexp
44671 wallispilem1
44781 wallispilem2
44782 wallispi
44786 stirlinglem15
44804 stirlingr
44806 dirker2re
44808 dirkerval2
44810 dirkerre
44811 dirkerper
44812 dirkertrigeqlem2
44815 dirkertrigeqlem3
44816 dirkertrigeq
44817 dirkeritg
44818 dirkercncflem1
44819 dirkercncflem2
44820 dirkercncflem4
44822 fourierdlem5
44828 fourierdlem9
44832 fourierdlem16
44839 fourierdlem18
44841 fourierdlem21
44844 fourierdlem22
44845 fourierdlem24
44847 fourierdlem38
44861 fourierdlem40
44863 fourierdlem43
44866 fourierdlem44
44867 fourierdlem46
44868 fourierdlem50
44872 fourierdlem58
44880 fourierdlem62
44884 fourierdlem66
44888 fourierdlem72
44894 fourierdlem74
44896 fourierdlem75
44897 fourierdlem76
44898 fourierdlem77
44899 fourierdlem78
44900 fourierdlem83
44905 fourierdlem85
44907 fourierdlem87
44909 fourierdlem88
44910 fourierdlem93
44915 fourierdlem94
44916 fourierdlem95
44917 fourierdlem101
44923 fourierdlem102
44924 fourierdlem103
44925 fourierdlem104
44926 fourierdlem111
44933 fourierdlem112
44934 fourierdlem113
44935 fourierdlem114
44936 sqwvfoura
44944 sqwvfourb
44945 fourierswlem
44946 fouriersw
44947 fouriercn
44948 |
