Colors of
variables: wff
setvar class |
Syntax hints:
= wceq 1542 ∈ wcel 2107
class class class wbr 5110 ‘cfv 6501
ℝcr 11057 0cc0 11058
1c1 11059 ≤ cle 11197
abscabs 15126 |
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 ax-pre-sup 11136 |
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-rmo 3356 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-sup 9385 df-pnf 11198 df-mnf 11199 df-xr 11200 df-ltxr 11201 df-le 11202 df-sub 11394 df-neg 11395 df-div 11820 df-nn 12161 df-2 12223
df-3 12224 df-n0 12421 df-z 12507
df-uz 12771 df-rp 12923 df-seq 13914 df-exp 13975 df-cj 14991 df-re 14992 df-im 14993 df-sqrt 15127 df-abs 15128 |
This theorem is referenced by: absexp
15196 absexpz
15197 iseraltlem3
15575 geolim
15762 geolim2
15763 georeclim
15764 geoisum1c
15772 efieq1re
16088 eirrlem
16093 3lcm2e6woprm
16498 4sqlem13
16836 4sqlem19
16842 gzrngunit
20879 ncvsm1
24534 dvlipcn
25374 dvfsumabs
25403 geolim3
25715 abelthlem1
25806 abelthlem2
25807 coskpi
25895 sineq0
25896 logtayl
26031 abscxpbnd
26122 root1cj
26125 bndatandm
26295 lgamgulmlem2
26395 lgamgulmlem5
26398 mule1
26513 logfacbnd3
26587 dchrabs
26624 zabsle1
26660 lgslem2
26662 lgsfcl2
26667 lgseisen
26743 2sqlem9
26791 2sqlem10
26792 nvm1
29649 nvmtri
29655 normlem7tALT
30103 norm-ii-i
30121 normsubi
30125 qqhval2lem
32602 qqh0
32605 subfaclim
33822 lcm1un
40499 nn0rppwr
40848 binomcxplemrat
42704 sineq0ALT
43293 fprodabs2
43910 |