| Colors of
variables: wff
setvar class |
| Syntax hints:
= wceq 1533 ∈ wcel 2098
class class class wbr 5139 ‘cfv 6534
ℝcr 11106 0cc0 11107
1c1 11108 ≤ cle 11247
abscabs 15179 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2695 ax-sep 5290 ax-nul 5297 ax-pow 5354 ax-pr 5418 ax-un 7719 ax-cnex 11163 ax-resscn 11164 ax-1cn 11165 ax-icn 11166 ax-addcl 11167 ax-addrcl 11168 ax-mulcl 11169 ax-mulrcl 11170 ax-mulcom 11171 ax-addass 11172 ax-mulass 11173 ax-distr 11174 ax-i2m1 11175 ax-1ne0 11176 ax-1rid 11177 ax-rnegex 11178 ax-rrecex 11179 ax-cnre 11180 ax-pre-lttri 11181 ax-pre-lttrn 11182 ax-pre-ltadd 11183 ax-pre-mulgt0 11184 ax-pre-sup 11185 |
| This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2526 df-eu 2555 df-clab 2702 df-cleq 2716 df-clel 2802 df-nfc 2877 df-ne 2933 df-nel 3039 df-ral 3054 df-rex 3063 df-rmo 3368 df-reu 3369 df-rab 3425 df-v 3468 df-sbc 3771 df-csb 3887 df-dif 3944 df-un 3946 df-in 3948 df-ss 3958 df-pss 3960 df-nul 4316 df-if 4522 df-pw 4597 df-sn 4622 df-pr 4624 df-op 4628 df-uni 4901 df-iun 4990 df-br 5140 df-opab 5202 df-mpt 5223 df-tr 5257 df-id 5565 df-eprel 5571 df-po 5579 df-so 5580 df-fr 5622 df-we 5624 df-xp 5673 df-rel 5674 df-cnv 5675 df-co 5676 df-dm 5677 df-rn 5678 df-res 5679 df-ima 5680 df-pred 6291 df-ord 6358 df-on 6359 df-lim 6360 df-suc 6361 df-iota 6486 df-fun 6536 df-fn 6537 df-f 6538 df-f1 6539 df-fo 6540 df-f1o 6541 df-fv 6542 df-riota 7358 df-ov 7405 df-oprab 7406 df-mpo 7407 df-om 7850 df-2nd 7970 df-frecs 8262 df-wrecs 8293 df-recs 8367 df-rdg 8406 df-er 8700 df-en 8937 df-dom 8938 df-sdom 8939 df-sup 9434 df-pnf 11248 df-mnf 11249 df-xr 11250 df-ltxr 11251 df-le 11252 df-sub 11444 df-neg 11445 df-div 11870 df-nn 12211 df-2 12273
df-3 12274 df-n0 12471 df-z 12557
df-uz 12821 df-rp 12973 df-seq 13965 df-exp 14026 df-cj 15044 df-re 15045 df-im 15046 df-sqrt 15180 df-abs 15181 |
| This theorem is referenced by: absexp
15249 absexpz
15250 iseraltlem3
15628 geolim
15814 geolim2
15815 georeclim
15816 geoisum1c
15824 efieq1re
16141 eirrlem
16146 3lcm2e6woprm
16551 4sqlem13
16891 4sqlem19
16897 gzrngunit
21297 ncvsm1
25006 dvlipcn
25851 dvfsumabs
25881 geolim3
26195 abelthlem1
26287 abelthlem2
26288 coskpi
26376 sineq0
26377 logtayl
26513 abscxpbnd
26607 root1cj
26610 bndatandm
26780 lgamgulmlem2
26881 lgamgulmlem5
26884 mule1
26999 logfacbnd3
27075 dchrabs
27112 zabsle1
27148 lgslem2
27150 lgsfcl2
27155 lgseisen
27231 2sqlem9
27279 2sqlem10
27280 nvm1
30390 nvmtri
30396 normlem7tALT
30844 norm-ii-i
30862 normsubi
30866 qqhval2lem
33453 qqh0
33456 subfaclim
34670 lcm1un
41375 nn0rppwr
41725 binomcxplemrat
43623 sineq0ALT
44212 fprodabs2
44821 |
