| Colors of
variables: wff
setvar class |
| Syntax hints:
= wceq 1534 ∈ wcel 2099
class class class wbr 5142 ‘cfv 6542
ℝcr 11131 0cc0 11132
1c1 11133 ≤ cle 11273
abscabs 15207 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906
ax-6 1964 ax-7 2004 ax-8 2101
ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2699 ax-sep 5293 ax-nul 5300 ax-pow 5359 ax-pr 5423 ax-un 7734 ax-cnex 11188 ax-resscn 11189 ax-1cn 11190 ax-icn 11191 ax-addcl 11192 ax-addrcl 11193 ax-mulcl 11194 ax-mulrcl 11195 ax-mulcom 11196 ax-addass 11197 ax-mulass 11198 ax-distr 11199 ax-i2m1 11200 ax-1ne0 11201 ax-1rid 11202 ax-rnegex 11203 ax-rrecex 11204 ax-cnre 11205 ax-pre-lttri 11206 ax-pre-lttrn 11207 ax-pre-ltadd 11208 ax-pre-mulgt0 11209 ax-pre-sup 11210 |
| This theorem depends on definitions:
df-bi 206 df-an 396
df-or 847 df-3or 1086 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2530 df-eu 2559 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2937 df-nel 3043 df-ral 3058 df-rex 3067 df-rmo 3372 df-reu 3373 df-rab 3429 df-v 3472 df-sbc 3776 df-csb 3891 df-dif 3948 df-un 3950 df-in 3952 df-ss 3962 df-pss 3964 df-nul 4319 df-if 4525 df-pw 4600 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-iun 4993 df-br 5143 df-opab 5205 df-mpt 5226 df-tr 5260 df-id 5570 df-eprel 5576 df-po 5584 df-so 5585 df-fr 5627 df-we 5629 df-xp 5678 df-rel 5679 df-cnv 5680 df-co 5681 df-dm 5682 df-rn 5683 df-res 5684 df-ima 5685 df-pred 6299 df-ord 6366 df-on 6367 df-lim 6368 df-suc 6369 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-f1 6547 df-fo 6548 df-f1o 6549 df-fv 6550 df-riota 7370 df-ov 7417 df-oprab 7418 df-mpo 7419 df-om 7865 df-2nd 7988 df-frecs 8280 df-wrecs 8311 df-recs 8385 df-rdg 8424 df-er 8718 df-en 8958 df-dom 8959 df-sdom 8960 df-sup 9459 df-pnf 11274 df-mnf 11275 df-xr 11276 df-ltxr 11277 df-le 11278 df-sub 11470 df-neg 11471 df-div 11896 df-nn 12237 df-2 12299
df-3 12300 df-n0 12497 df-z 12583
df-uz 12847 df-rp 13001 df-seq 13993 df-exp 14053 df-cj 15072 df-re 15073 df-im 15074 df-sqrt 15208 df-abs 15209 |
| This theorem is referenced by: absexp
15277 absexpz
15278 iseraltlem3
15656 geolim
15842 geolim2
15843 georeclim
15844 geoisum1c
15852 efieq1re
16169 eirrlem
16174 3lcm2e6woprm
16579 4sqlem13
16919 4sqlem19
16925 gzrngunit
21359 ncvsm1
25075 dvlipcn
25920 dvfsumabs
25950 geolim3
26267 abelthlem1
26361 abelthlem2
26362 coskpi
26450 sineq0
26451 logtayl
26587 abscxpbnd
26681 root1cj
26684 bndatandm
26854 lgamgulmlem2
26955 lgamgulmlem5
26958 mule1
27073 logfacbnd3
27149 dchrabs
27186 zabsle1
27222 lgslem2
27224 lgsfcl2
27229 lgseisen
27305 2sqlem9
27353 2sqlem10
27354 nvm1
30468 nvmtri
30474 normlem7tALT
30922 norm-ii-i
30940 normsubi
30944 qqhval2lem
33576 qqh0
33579 subfaclim
34792 lcm1un
41478 nn0rppwr
41887 binomcxplemrat
43781 sineq0ALT
44370 fprodabs2
44977 |
