Colors of
variables: wff
setvar class |
Syntax hints:
= wceq 1539 ∈ wcel 2104
‘cfv 6458 (class class class)co 7307
ℂcc 10915 0cc0 10917
· cmul 10922 ∗ccj 14852 √csqrt 14989 abscabs 14990 |
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 2707 ax-sep 5232 ax-nul 5239 ax-pow 5297 ax-pr 5361 ax-un 7620 ax-cnex 10973 ax-resscn 10974 ax-1cn 10975 ax-icn 10976 ax-addcl 10977 ax-addrcl 10978 ax-mulcl 10979 ax-mulrcl 10980 ax-mulcom 10981 ax-addass 10982 ax-mulass 10983 ax-distr 10984 ax-i2m1 10985 ax-1ne0 10986 ax-1rid 10987 ax-rnegex 10988 ax-rrecex 10989 ax-cnre 10990 ax-pre-lttri 10991 ax-pre-lttrn 10992 ax-pre-ltadd 10993 ax-pre-mulgt0 10994 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 846 df-3or 1088 df-3an 1089 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2538 df-eu 2567 df-clab 2714 df-cleq 2728 df-clel 2814 df-nfc 2887 df-ne 2942 df-nel 3048 df-ral 3063 df-rex 3072 df-rmo 3285 df-reu 3286 df-rab 3287 df-v 3439 df-sbc 3722 df-csb 3838 df-dif 3895 df-un 3897 df-in 3899 df-ss 3909 df-pss 3911 df-nul 4263 df-if 4466 df-pw 4541 df-sn 4566 df-pr 4568 df-op 4572 df-uni 4845 df-iun 4933 df-br 5082 df-opab 5144 df-mpt 5165 df-tr 5199 df-id 5500 df-eprel 5506 df-po 5514 df-so 5515 df-fr 5555 df-we 5557 df-xp 5606 df-rel 5607 df-cnv 5608 df-co 5609 df-dm 5610 df-rn 5611 df-res 5612 df-ima 5613 df-pred 6217 df-ord 6284 df-on 6285 df-lim 6286 df-suc 6287 df-iota 6410 df-fun 6460 df-fn 6461 df-f 6462 df-f1 6463 df-fo 6464 df-f1o 6465 df-fv 6466 df-riota 7264 df-ov 7310 df-oprab 7311 df-mpo 7312 df-om 7745 df-2nd 7864 df-frecs 8128 df-wrecs 8159 df-recs 8233 df-rdg 8272 df-er 8529 df-en 8765 df-dom 8766 df-sdom 8767 df-pnf 11057 df-mnf 11058 df-xr 11059 df-ltxr 11060 df-le 11061 df-sub 11253 df-neg 11254 df-div 11679 df-nn 12020 df-2 12082
df-n0 12280 df-z 12366
df-uz 12629 df-rp 12777 df-seq 13768 df-exp 13829 df-cj 14855 df-re 14856 df-im 14857 df-sqrt 14991 df-abs 14992 |
This theorem is referenced by: abs00
15046 abs1m
15092 climconst
15297 rlimconst
15298 fsumabs
15558 georeclim
15629 geoisumr
15635 dvdsabseq
16067 gcd0id
16271 lcmid
16359 4sqlem19
16709 absabv
20700 gzrngunit
20709 zringunit
20733 aannenlem2
25534 aalioulem3
25539 tanabsge
25708 sinkpi
25723 sineq0
25725 isosctrlem2
26014 lgamgulmlem1
26223 ftalem3
26269 mule1
26342 zabsle1
26489 lgslem2
26491 lgsfcl2
26496 bcsiALT
29586 0cnfn
30387 nmfn0
30394 nmophmi
30438 nmcfnexi
30458 dnizeq0
34700 unbdqndv2lem2
34735 mblfinlem2
35859 ftc1anclem7
35900 ftc1anclem8
35901 ftc1anc
35902 dvgrat
41968 radcnvrat
41970 sineq0ALT
42595 constlimc
43214 0cnv
43332 |