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Mirrors > Home > MPE Home > Th. List > atanval | Structured version Visualization version Unicode version |
Description: Value of the arctan function. (Contributed by Mario Carneiro, 31-Mar-2015.) |
Ref | Expression |
---|---|
atanval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 6323 |
. . . . . . 7
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2 | 1 | oveq2d 6331 |
. . . . . 6
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3 | 2 | fveq2d 5892 |
. . . . 5
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4 | 1 | oveq2d 6331 |
. . . . . 6
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5 | 4 | fveq2d 5892 |
. . . . 5
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6 | 3, 5 | oveq12d 6333 |
. . . 4
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7 | 6 | oveq2d 6331 |
. . 3
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8 | df-atan 23842 |
. . 3
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9 | ovex 6343 |
. . 3
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10 | 7, 8, 9 | fvmpt 5971 |
. 2
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11 | atanf 23855 |
. . 3
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12 | 11 | fdmi 5757 |
. 2
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13 | 10, 12 | eleq2s 2558 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-rep 4529 ax-sep 4539 ax-nul 4548 ax-pow 4595 ax-pr 4653 ax-un 6610 ax-inf2 8172 ax-cnex 9621 ax-resscn 9622 ax-1cn 9623 ax-icn 9624 ax-addcl 9625 ax-addrcl 9626 ax-mulcl 9627 ax-mulrcl 9628 ax-mulcom 9629 ax-addass 9630 ax-mulass 9631 ax-distr 9632 ax-i2m1 9633 ax-1ne0 9634 ax-1rid 9635 ax-rnegex 9636 ax-rrecex 9637 ax-cnre 9638 ax-pre-lttri 9639 ax-pre-lttrn 9640 ax-pre-ltadd 9641 ax-pre-mulgt0 9642 ax-pre-sup 9643 ax-addf 9644 ax-mulf 9645 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1458 df-fal 1461 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-nel 2636 df-ral 2754 df-rex 2755 df-reu 2756 df-rmo 2757 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-pss 3432 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-tp 3985 df-op 3987 df-uni 4213 df-int 4249 df-iun 4294 df-iin 4295 df-br 4417 df-opab 4476 df-mpt 4477 df-tr 4512 df-eprel 4764 df-id 4768 df-po 4774 df-so 4775 df-fr 4812 df-se 4813 df-we 4814 df-xp 4859 df-rel 4860 df-cnv 4861 df-co 4862 df-dm 4863 df-rn 4864 df-res 4865 df-ima 4866 df-pred 5399 df-ord 5445 df-on 5446 df-lim 5447 df-suc 5448 df-iota 5565 df-fun 5603 df-fn 5604 df-f 5605 df-f1 5606 df-fo 5607 df-f1o 5608 df-fv 5609 df-isom 5610 df-riota 6277 df-ov 6318 df-oprab 6319 df-mpt2 6320 df-of 6558 df-om 6720 df-1st 6820 df-2nd 6821 df-supp 6942 df-wrecs 7054 df-recs 7116 df-rdg 7154 df-1o 7208 df-2o 7209 df-oadd 7212 df-er 7389 df-map 7500 df-pm 7501 df-ixp 7549 df-en 7596 df-dom 7597 df-sdom 7598 df-fin 7599 df-fsupp 7910 df-fi 7951 df-sup 7982 df-inf 7983 df-oi 8051 df-card 8399 df-cda 8624 df-pnf 9703 df-mnf 9704 df-xr 9705 df-ltxr 9706 df-le 9707 df-sub 9888 df-neg 9889 df-div 10298 df-nn 10638 df-2 10696 df-3 10697 df-4 10698 df-5 10699 df-6 10700 df-7 10701 df-8 10702 df-9 10703 df-10 10704 df-n0 10899 df-z 10967 df-dec 11081 df-uz 11189 df-q 11294 df-rp 11332 df-xneg 11438 df-xadd 11439 df-xmul 11440 df-ioo 11668 df-ioc 11669 df-ico 11670 df-icc 11671 df-fz 11814 df-fzo 11947 df-fl 12060 df-mod 12129 df-seq 12246 df-exp 12305 df-fac 12492 df-bc 12520 df-hash 12548 df-shft 13179 df-cj 13211 df-re 13212 df-im 13213 df-sqrt 13347 df-abs 13348 df-limsup 13575 df-clim 13601 df-rlim 13602 df-sum 13802 df-ef 14170 df-sin 14172 df-cos 14173 df-pi 14175 df-struct 15172 df-ndx 15173 df-slot 15174 df-base 15175 df-sets 15176 df-ress 15177 df-plusg 15252 df-mulr 15253 df-starv 15254 df-sca 15255 df-vsca 15256 df-ip 15257 df-tset 15258 df-ple 15259 df-ds 15261 df-unif 15262 df-hom 15263 df-cco 15264 df-rest 15370 df-topn 15371 df-0g 15389 df-gsum 15390 df-topgen 15391 df-pt 15392 df-prds 15395 df-xrs 15449 df-qtop 15455 df-imas 15456 df-xps 15459 df-mre 15541 df-mrc 15542 df-acs 15544 df-mgm 16537 df-sgrp 16576 df-mnd 16586 df-submnd 16632 df-mulg 16725 df-cntz 17020 df-cmn 17481 df-psmet 19011 df-xmet 19012 df-met 19013 df-bl 19014 df-mopn 19015 df-fbas 19016 df-fg 19017 df-cnfld 19020 df-top 19970 df-bases 19971 df-topon 19972 df-topsp 19973 df-cld 20083 df-ntr 20084 df-cls 20085 df-nei 20163 df-lp 20201 df-perf 20202 df-cn 20292 df-cnp 20293 df-haus 20380 df-tx 20626 df-hmeo 20819 df-fil 20910 df-fm 21002 df-flim 21003 df-flf 21004 df-xms 21384 df-ms 21385 df-tms 21386 df-cncf 21959 df-limc 22870 df-dv 22871 df-log 23555 df-atan 23842 |
This theorem is referenced by: atanneg 23882 atancj 23885 efiatan 23887 efiatan2 23892 2efiatan 23893 atantan 23898 atanbndlem 23900 atantayl 23912 log2cnv 23919 |
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