Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2107
(class class class)co 7362 ℂcc 11056
2c2 12215 ↑cexp 13974 |
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 2708 ax-sep 5261 ax-nul 5268 ax-pow 5325 ax-pr 5389 ax-un 7677 ax-cnex 11114 ax-resscn 11115 ax-1cn 11116 ax-icn 11117 ax-addcl 11118 ax-addrcl 11119 ax-mulcl 11120 ax-mulrcl 11121 ax-mulcom 11122 ax-addass 11123 ax-mulass 11124 ax-distr 11125 ax-i2m1 11126 ax-1ne0 11127 ax-1rid 11128 ax-rnegex 11129 ax-rrecex 11130 ax-cnre 11131 ax-pre-lttri 11132 ax-pre-lttrn 11133 ax-pre-ltadd 11134 ax-pre-mulgt0 11135 |
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 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ne 2945 df-nel 3051 df-ral 3066 df-rex 3075 df-reu 3357 df-rab 3411 df-v 3450 df-sbc 3745 df-csb 3861 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-pss 3934 df-nul 4288 df-if 4492 df-pw 4567 df-sn 4592 df-pr 4594 df-op 4598 df-uni 4871 df-iun 4961 df-br 5111 df-opab 5173 df-mpt 5194 df-tr 5228 df-id 5536 df-eprel 5542 df-po 5550 df-so 5551 df-fr 5593 df-we 5595 df-xp 5644 df-rel 5645 df-cnv 5646 df-co 5647 df-dm 5648 df-rn 5649 df-res 5650 df-ima 5651 df-pred 6258 df-ord 6325 df-on 6326 df-lim 6327 df-suc 6328 df-iota 6453 df-fun 6503 df-fn 6504 df-f 6505 df-f1 6506 df-fo 6507 df-f1o 6508 df-fv 6509 df-riota 7318 df-ov 7365 df-oprab 7366 df-mpo 7367 df-om 7808 df-2nd 7927 df-frecs 8217 df-wrecs 8248 df-recs 8322 df-rdg 8361 df-er 8655 df-en 8891 df-dom 8892 df-sdom 8893 df-pnf 11198 df-mnf 11199 df-xr 11200 df-ltxr 11201 df-le 11202 df-sub 11394 df-neg 11395 df-nn 12161 df-2 12223
df-n0 12421 df-z 12507
df-uz 12771 df-seq 13914 df-exp 13975 |
This theorem is referenced by: mulsubdivbinom2
14169 muldivbinom2
14170 recval
15214 bhmafibid1cn
15355 bhmafibid2cn
15356 bhmafibid2
15358 arisum2
15753 fsumcube
15950 efi4p
16026 sincossq
16065 cos2t
16067 cos2tsin
16068 sqrt2irrlem
16137 pythagtriplem1
16695 pythagtriplem2
16696 pythagtriplem6
16700 pythagtriplem7
16701 pythagtriplem12
16705 pythagtriplem14
16707 4sqlem7
16823 4sqlem10
16826 4sqlem14
16837 4cphipval2
24622 csbren
24779 rrxmval
24785 rrxmetlem
24787 dvrecg
25353 dvmptdiv
25354 dveflem
25359 coskpi
25895 coseq1
25897 tanregt0
25911 efif1olem4
25917 tanarg
25990 lawcoslem1
26181 lawcos
26182 pythag
26183 ssscongptld
26188 chordthmlem3
26200 chordthmlem4
26201 chordthmlem5
26202 heron
26204 quad2
26205 quad
26206 dcubic1lem
26209 dcubic2
26210 dcubic1
26211 dcubic
26212 mcubic
26213 cubic2
26214 cubic
26215 binom4
26216 dquartlem1
26217 dquartlem2
26218 dquart
26219 quart1cl
26220 quart1lem
26221 quart1
26222 quartlem1
26223 quartlem2
26224 quartlem4
26226 quart
26227 asinlem3
26237 asinneg
26252 asinsin
26258 atandmcj
26275 efiatan2
26283 atandmtan
26286 cosatan
26287 cosatanne0
26288 dvatan
26301 cxp2limlem
26341 lgamgulmlem4
26397 basellem8
26453 lgsdir
26696 2sqlem4
26785 2sqlem11
26793 2sqn0
26798 2sqmod
26800 2sqnn
26803 addsq2reu
26804 2sqreultlem
26811 2sqreunnltlem
26814 2sqreulem2
26816 mulog2sumlem2
26899 mulog2sumlem3
26900 logsqvma
26906 selberglem1
26909 selberglem3
26911 selberg
26912 logdivbnd
26920 pntlemf
26969 pntlemk
26970 pntlemo
26971 ax5seglem1
27919 ax5seglem2
27920 ax5seglem6
27925 ax5seglem9
27928 axlowdimlem16
27948 axlowdimlem17
27949 4ipval2
29692 ipidsq
29694 cncph
29803 hhph
30162 eigvalcl
30945 circlemethhgt
33296 hgt750leme
33311 sin2h
36097 cos2h
36098 tan2h
36099 dvtan
36157 dvasin
36191 dvacos
36192 areacirclem1
36195 areacirclem2
36196 areacirclem4
36198 areacirc
36200 ismrer1
36326 aks4d1p1p2
40556 aks4d1p1p6
40559 aks4d1p1p7
40560 aks4d1p1p5
40561 cu3addd
41032 3cubeslem2
41037 3cubeslem3l
41038 3cubeslem3r
41039 3cubeslem4
41041 pellexlem1
41181 pellexlem2
41182 pellexlem6
41186 pell1qrge1
41222 pell1qrgaplem
41225 rmspecsqrtnq
41258 rmxdbl
41292 jm2.18
41341 jm2.19lem1
41342 jm2.25
41352 jm2.27c
41360 sqrtcval
41987 dvdivf
44237 dvdivbd
44238 itgsinexplem1
44269 itgsinexp
44270 wallispi2lem1
44386 wallispi2lem2
44387 wallispi2
44388 stirlinglem1
44389 stirlinglem3
44391 stirlinglem8
44396 stirlinglem10
44398 stirlinglem15
44403 rrxtopnfi
44602 hoiqssbllem2
44938 quad1
45886 itschlc0yqe
46920 itsclc0yqsollem1
46922 itsclc0yqsol
46924 itscnhlc0xyqsol
46925 itschlc0xyqsol1
46926 itschlc0xyqsol
46927 itsclc0xyqsolr
46929 2itscplem1
46938 2itscplem3
46940 itscnhlinecirc02plem1
46942 onetansqsecsq
47280 cotsqcscsq
47281 |