Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2107
class class class wbr 5109 (class class class)co 7361
ℝcr 11058 1c1 11060
< clt 11197 −
cmin 11393 |
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 2704 ax-sep 5260 ax-nul 5267 ax-pow 5324 ax-pr 5388 ax-un 7676 ax-resscn 11116 ax-1cn 11117 ax-icn 11118 ax-addcl 11119 ax-addrcl 11120 ax-mulcl 11121 ax-mulrcl 11122 ax-mulcom 11123 ax-addass 11124 ax-mulass 11125 ax-distr 11126 ax-i2m1 11127 ax-1ne0 11128 ax-1rid 11129 ax-rnegex 11130 ax-rrecex 11131 ax-cnre 11132 ax-pre-lttri 11133 ax-pre-lttrn 11134 ax-pre-ltadd 11135 ax-pre-mulgt0 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 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-reu 3353 df-rab 3407 df-v 3449 df-sbc 3744 df-csb 3860 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-pw 4566 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-br 5110 df-opab 5172 df-mpt 5193 df-id 5535 df-po 5549 df-so 5550 df-xp 5643 df-rel 5644 df-cnv 5645 df-co 5646 df-dm 5647 df-rn 5648 df-res 5649 df-ima 5650 df-iota 6452 df-fun 6502 df-fn 6503 df-f 6504 df-f1 6505 df-fo 6506 df-f1o 6507 df-fv 6508 df-riota 7317 df-ov 7364 df-oprab 7365 df-mpo 7366 df-er 8654 df-en 8890 df-dom 8891 df-sdom 8892 df-pnf 11199 df-mnf 11200 df-xr 11201 df-ltxr 11202 df-le 11203 df-sub 11395 df-neg 11396 |
This theorem is referenced by: suprzcl
12591 fzsuc2
13508 fzm1
13530 m1modnnsub1
13831 cshwidxm1
14704 fsumm1
15644 isumsplit
15733 climcndslem1
15742 bitsfzolem
16322 fldivp1
16777 4sqlem12
16836 ram0
16902 sylow1lem1
19388 dgreq0
25649 atanlogsublem
26288 birthdaylem3
26326 wilthlem1
26440 ftalem5
26449 basellem5
26457 lgsval2lem
26678 lgsqrlem2
26718 gausslemma2dlem0c
26729 lgsquadlem1
26751 lgsquadlem2
26752 pntrsumbnd2
26938 axlowdimlem16
27955 pthdlem1
28763 clwwlkel
29039 clwwlknonex2lem2
29101 xlt2addrd
31717 cycpmco2lem6
32036 cvmliftlem6
33948 cvmliftlem8
33950 cvmliftlem9
33951 cvmliftlem10
33952 bcprod
34374 iooelexlt
35883 poimirlem1
36129 poimirlem2
36130 poimirlem6
36134 poimirlem7
36135 poimirlem8
36136 poimirlem12
36140 poimirlem15
36143 poimirlem16
36144 poimirlem17
36145 poimirlem19
36147 poimirlem20
36148 poimirlem21
36149 poimirlem22
36150 poimirlem23
36151 poimirlem26
36154 mettrifi
36266 aks4d1p1
40583 sticksstones10
40613 sticksstones12a
40615 metakunt18
40644 metakunt20
40646 metakunt24
40650 irrapxlem1
41192 rmspecsqrtnq
41276 acongeq
41354 monoords
43622 fzisoeu
43625 fzdifsuc2
43635 infleinflem2
43696 unb2ltle
43740 limsupre3lem
44063 xlimxrre
44162 xlimmnfv
44165 iblspltprt
44304 itgspltprt
44310 stoweidlem11
44342 stoweidlem14
44345 fourierdlem11
44449 fourierdlem12
44450 fourierdlem15
44453 fourierdlem41
44479 fourierdlem48
44485 fourierdlem49
44486 fourierdlem50
44487 fourierdlem79
44516 ioorrnopnxrlem
44637 iundjiun
44791 lswn0
45726 bgoldbtbndlem4
46090 m1modmmod
46697 logbpw2m1
46743 |