| Colors of
variables: wff
setvar class |
| Syntax hints:
∈ wcel 2098 (class class class)co 7426
ℝcr 11147 / cdiv 11911
2c2 12307 πcpi 16052 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2699 ax-rep 5289 ax-sep 5303 ax-nul 5310 ax-pow 5369 ax-pr 5433 ax-un 7748 ax-inf2 9674 ax-cnex 11204 ax-resscn 11205 ax-1cn 11206 ax-icn 11207 ax-addcl 11208 ax-addrcl 11209 ax-mulcl 11210 ax-mulrcl 11211 ax-mulcom 11212 ax-addass 11213 ax-mulass 11214 ax-distr 11215 ax-i2m1 11216 ax-1ne0 11217 ax-1rid 11218 ax-rnegex 11219 ax-rrecex 11220 ax-cnre 11221 ax-pre-lttri 11222 ax-pre-lttrn 11223 ax-pre-ltadd 11224 ax-pre-mulgt0 11225 ax-pre-sup 11226 ax-addf 11227 |
| This theorem depends on definitions:
df-bi 206 df-an 395
df-or 846 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2529 df-eu 2558 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2938 df-nel 3044 df-ral 3059 df-rex 3068 df-rmo 3374 df-reu 3375 df-rab 3431 df-v 3475 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-pss 3968 df-nul 4327 df-if 4533 df-pw 4608 df-sn 4633 df-pr 4635 df-tp 4637 df-op 4639 df-uni 4913 df-int 4954 df-iun 5002 df-iin 5003 df-br 5153 df-opab 5215 df-mpt 5236 df-tr 5270 df-id 5580 df-eprel 5586 df-po 5594 df-so 5595 df-fr 5637 df-se 5638 df-we 5639 df-xp 5688 df-rel 5689 df-cnv 5690 df-co 5691 df-dm 5692 df-rn 5693 df-res 5694 df-ima 5695 df-pred 6310 df-ord 6377 df-on 6378 df-lim 6379 df-suc 6380 df-iota 6505 df-fun 6555 df-fn 6556 df-f 6557 df-f1 6558 df-fo 6559 df-f1o 6560 df-fv 6561 df-isom 6562 df-riota 7382 df-ov 7429 df-oprab 7430 df-mpo 7431 df-of 7692 df-om 7879 df-1st 8001 df-2nd 8002 df-supp 8174 df-frecs 8295 df-wrecs 8326 df-recs 8400 df-rdg 8439 df-1o 8495 df-2o 8496 df-er 8733 df-map 8855 df-pm 8856 df-ixp 8925 df-en 8973 df-dom 8974 df-sdom 8975 df-fin 8976 df-fsupp 9396 df-fi 9444 df-sup 9475 df-inf 9476 df-oi 9543 df-card 9972 df-pnf 11290 df-mnf 11291 df-xr 11292 df-ltxr 11293 df-le 11294 df-sub 11486 df-neg 11487 df-div 11912 df-nn 12253 df-2 12315
df-3 12316 df-4 12317
df-5 12318 df-6 12319
df-7 12320 df-8 12321
df-9 12322 df-n0 12513 df-z 12599
df-dec 12718 df-uz 12863 df-q 12973
df-rp 13017 df-xneg 13134 df-xadd 13135 df-xmul 13136 df-ioo 13370 df-ioc 13371 df-ico 13372 df-icc 13373 df-fz 13527 df-fzo 13670 df-fl 13799 df-seq 14009 df-exp 14069 df-fac 14275 df-bc 14304 df-hash 14332 df-shft 15056 df-cj 15088 df-re 15089 df-im 15090 df-sqrt 15224 df-abs 15225 df-limsup 15457 df-clim 15474 df-rlim 15475 df-sum 15675 df-ef 16053 df-sin 16055 df-cos 16056 df-pi 16058 df-struct 17125 df-sets 17142 df-slot 17160 df-ndx 17172 df-base 17190 df-ress 17219 df-plusg 17255 df-mulr 17256 df-starv 17257 df-sca 17258 df-vsca 17259 df-ip 17260 df-tset 17261 df-ple 17262 df-ds 17264 df-unif 17265 df-hom 17266 df-cco 17267 df-rest 17413 df-topn 17414 df-0g 17432 df-gsum 17433 df-topgen 17434 df-pt 17435 df-prds 17438 df-xrs 17493 df-qtop 17498 df-imas 17499 df-xps 17501 df-mre 17575 df-mrc 17576 df-acs 17578 df-mgm 18609 df-sgrp 18688 df-mnd 18704 df-submnd 18750 df-mulg 19038 df-cntz 19282 df-cmn 19751 df-psmet 21285 df-xmet 21286 df-met 21287 df-bl 21288 df-mopn 21289 df-fbas 21290 df-fg 21291 df-cnfld 21294 df-top 22824 df-topon 22841 df-topsp 22863 df-bases 22877 df-cld 22951 df-ntr 22952 df-cls 22953 df-nei 23030 df-lp 23068 df-perf 23069 df-cn 23159 df-cnp 23160 df-haus 23247 df-tx 23494 df-hmeo 23687 df-fil 23778 df-fm 23870 df-flim 23871 df-flf 23872 df-xms 24254 df-ms 24255 df-tms 24256 df-cncf 24826 df-limc 25823 df-dv 25824 |
| This theorem is referenced by: neghalfpire
26428 cosneghalfpi
26433 sinhalfpip
26455 sinhalfpim
26456 coshalfpip
26457 coshalfpim
26458 sincosq1lem
26460 sincosq1sgn
26461 sincosq2sgn
26462 sincosq3sgn
26463 sincosq4sgn
26464 coseq00topi
26465 coseq0negpitopi
26466 tanabsge
26469 cosq14gt0
26473 cosq14ge0
26474 sincos6thpi
26478 cosne0
26491 sinord
26496 resinf1o
26498 tanord1
26499 tanord
26500 tanregt0
26501 efif1olem4
26507 logi
26549 argregt0
26572 argrege0
26573 logimul
26576 isosctrlem1
26778 asinsinlem
26851 asinsin
26852 acoscos
26853 asin1
26854 reasinsin
26856 acosbnd
26860 asinrecl
26862 acosrecl
26863 atanlogsublem
26875 atantan
26883 atanbndlem
26885 atanbnd
26886 atan1
26888 basellem4
27044 iexpire
35370 cos2h
37125 tan2h
37126 dvacos
37219 fourierdlem62
45603 |
