| Colors of
variables: wff
setvar class |
| Syntax hints:
= wceq 1539 ∈ wcel 2104
(class class class)co 7413 1c1 11115
2c2 12273 ℤcz 12564
↑cexp 14033 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911
ax-6 1969 ax-7 2009 ax-8 2106
ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5300 ax-nul 5307 ax-pow 5364 ax-pr 5428 ax-un 7729 ax-cnex 11170 ax-resscn 11171 ax-1cn 11172 ax-icn 11173 ax-addcl 11174 ax-addrcl 11175 ax-mulcl 11176 ax-mulrcl 11177 ax-mulcom 11178 ax-addass 11179 ax-mulass 11180 ax-distr 11181 ax-i2m1 11182 ax-1ne0 11183 ax-1rid 11184 ax-rnegex 11185 ax-rrecex 11186 ax-cnre 11187 ax-pre-lttri 11188 ax-pre-lttrn 11189 ax-pre-ltadd 11190 ax-pre-mulgt0 11191 |
| This theorem depends on definitions:
df-bi 206 df-an 395
df-or 844 df-3or 1086 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-ne 2939 df-nel 3045 df-ral 3060 df-rex 3069 df-rmo 3374 df-reu 3375 df-rab 3431 df-v 3474 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-op 4636 df-uni 4910 df-iun 5000 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-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-riota 7369 df-ov 7416 df-oprab 7417 df-mpo 7418 df-om 7860 df-2nd 7980 df-frecs 8270 df-wrecs 8301 df-recs 8375 df-rdg 8414 df-er 8707 df-en 8944 df-dom 8945 df-sdom 8946 df-pnf 11256 df-mnf 11257 df-xr 11258 df-ltxr 11259 df-le 11260 df-sub 11452 df-neg 11453 df-div 11878 df-nn 12219 df-2 12281
df-n0 12479 df-z 12565
df-uz 12829 df-seq 13973 df-exp 14034 |
| This theorem is referenced by: neg1sqe1
14166 binom21
14188 binom2sub1
14190 sq01
14194 01sqrexlem1
15195 sqrt1
15224 sinbnd
16129 cosbnd
16130 cos1bnd
16136 cos2bnd
16137 cos01gt0
16140 sqnprm
16645 numdensq
16696 zsqrtelqelz
16700 prmreclem1
16855 prmreclem2
16856 4sqlem13
16896 4sqlem19
16902 odadd
19761 abvneg
20587 gzrngunitlem
21212 gzrngunit
21213 zringunit
21239 sinhalfpilem
26207 cos2pi
26220 tangtx
26249 coskpi
26266 tanregt0
26282 efif1olem3
26287 root1id
26496 root1cj
26498 isosctrlem2
26558 asin1
26633 efiatan2
26656 bndatandm
26668 atans2
26670 wilthlem1
26806 dchrinv
26998 sum2dchr
27011 lgslem1
27034 lgsne0
27072 lgssq
27074 lgssq2
27075 1lgs
27077 lgs1
27078 lgsdinn0
27082 lgsquad2lem2
27122 lgsquad3
27124 2lgsoddprmlem3a
27147 2sqlem9
27164 2sqlem10
27165 2sqlem11
27166 2sqblem
27168 2sqb
27169 2sq2
27170 addsqn2reu
27178 addsqrexnreu
27179 addsq2nreurex
27181 mulog2sumlem2
27272 pntlemb
27334 axlowdimlem16
28480 ex-pr
29948 normlem1
30628 kbpj
31474 hstnmoc
31741 hstle1
31744 hst1h
31745 hstle
31748 strlem3a
31770 strlem4
31772 strlem5
31773 jplem1
31786 dvasin
36877 dvacos
36878 areacirclem1
36881 areacirc
36886 cntotbnd
36969 3cubeslem1
41726 3cubeslem2
41727 3cubeslem3r
41729 pell1qrge1
41912 pell1qr1
41913 pell1qrgaplem
41915 pell14qrgapw
41918 pellqrex
41921 rmspecnonsq
41949 rmspecfund
41951 rmspecpos
41959 sqrtcval
42696 stoweidlem1
45017 wallispi2lem2
45088 stirlinglem10
45099 lighneallem2
46574 onetansqsecsq
47895 cotsqcscsq
47896 |
