Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1540
∈ wcel 2105 ‘cfv 6543 (class class class)co 7412
ℂcc 11111 −
cmin 11449 abscabs 15186 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912
ax-6 1970 ax-7 2010 ax-8 2107
ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7728 ax-resscn 11170 ax-1cn 11171 ax-icn 11172 ax-addcl 11173 ax-addrcl 11174 ax-mulcl 11175 ax-mulrcl 11176 ax-mulcom 11177 ax-addass 11178 ax-mulass 11179 ax-distr 11180 ax-i2m1 11181 ax-1ne0 11182 ax-1rid 11183 ax-rnegex 11184 ax-rrecex 11185 ax-cnre 11186 ax-pre-lttri 11187 ax-pre-lttrn 11188 ax-pre-ltadd 11189 ax-pre-mulgt0 11190 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-nel 3046 df-ral 3061 df-rex 3070 df-rmo 3375 df-reu 3376 df-rab 3432 df-v 3475 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-br 5149 df-opab 5211 df-mpt 5232 df-id 5574 df-po 5588 df-so 5589 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-riota 7368 df-ov 7415 df-oprab 7416 df-mpo 7417 df-er 8706 df-en 8943 df-dom 8944 df-sdom 8945 df-pnf 11255 df-mnf 11256 df-xr 11257 df-ltxr 11258 df-le 11259 df-sub 11451 df-neg 11452 df-div 11877 df-2 12280
df-cj 15051 df-re 15052 df-im 15053 df-abs 15188 |
This theorem is referenced by: rlimuni
15499 climuni
15501 2clim
15521 rlimrecl
15529 subcn2
15544 reccn2
15546 climcau
15622 caucvgrlem
15624 serf0
15632 mertenslem2
15836 xrsxmet
24546 elcncf2
24631 cnllycmp
24703 dvlip
25746 c1lip1
25750 dvfsumrlim2
25785 dvfsum2
25787 ftc1a
25790 aalioulem3
26084 ulmcaulem
26143 ulmcau
26144 ulmbdd
26147 ulmcn
26148 ulmdvlem1
26149 logcnlem4
26390 ssscongptld
26564 chordthmlem3
26576 chordthmlem4
26577 lgamucov
26779 ftalem2
26815 logfacrlim
26964 dchrisumlem3
27231 dchrisum0lem1b
27255 mulog2sumlem2
27275 pntrlog2bndlem3
27319 smcnlem
30218 qqhucn
33271 dnibndlem2
35659 dnibndlem6
35663 dnibndlem8
35665 dnibnd
35671 unbdqndv2lem1
35689 knoppndvlem10
35701 knoppndvlem15
35706 ftc1anclem8
36872 irrapxlem3
41865 irrapxlem5
41867 pell14qrgt0
41900 acongeq
42025 absimlere
44489 limcrecl
44644 islpcn
44654 lptre2pt
44655 0ellimcdiv
44664 limclner
44666 dvbdfbdioolem2
44944 ioodvbdlimc1lem1
44946 ioodvbdlimc1lem2
44947 ioodvbdlimc2lem
44949 fourierdlem42
45164 ioorrnopnlem
45319 smflimlem4
45789 |