Colors of
variables: wff
setvar class |
Syntax hints: class class
class wbr 5109 (class class class)co 7361
0cc0 11059 1c1 11060
+ caddc 11062 <
clt 11197 2c2 12216 |
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 df-2 12224 |
This theorem is referenced by: 2ne0
12265 3pos
12266 halfgt0
12377 halflt1
12379 halfpos2
12390 halfnneg2
12392 nominpos
12398 avglt1
12399 avglt2
12400 nn0n0n1ge2b
12489 3halfnz
12590 2rp
12928 hashgt23el
14333 s3fv0
14789 sqreulem
15253 cos2bnd
16078 sin02gt0
16082 sincos2sgn
16084 sin4lt0
16085 epos
16097 sqrt2re
16140 nnoddm1d2
16276 2mulprm
16577 prmgaplem7
16937 slotsdifdsndx
17283 odrngstr
17292 imasvalstr
17341 psgnunilem2
19285 cnfldstr
20821 cnfldfunALTOLD
20833 bl2in
23776 iihalf1
24317 iihalf2
24319 pcoass
24410 tcphcphlem1
24622 trirn
24787 minveclem2
24813 minveclem4
24819 ovolunlem1a
24883 vitalilem4
24998 mbfi1fseqlem5
25107 pilem2
25834 pilem3
25835 pipos
25840 sinhalfpilem
25843 sincosq1lem
25877 tangtx
25885 sinq12gt0
25887 sincos6thpi
25895 cosordlem
25909 tanord1
25916 efif1olem2
25922 efif1olem4
25924 cxpcn3lem
26123 ang180lem1
26182 ang180lem2
26183 atantan
26296 atanbndlem
26298 atans2
26304 leibpi
26315 log2tlbnd
26318 basellem1
26453 basellem2
26454 basellem3
26455 ppiltx
26549 ppiub
26575 chtublem
26582 chtub
26583 chpval2
26589 bcmono
26648 bpos1lem
26653 bposlem1
26655 bposlem2
26656 bposlem3
26657 bposlem4
26658 bposlem5
26659 bposlem6
26660 bposlem7
26661 gausslemma2dlem0c
26729 gausslemma2dlem1a
26736 gausslemma2dlem2
26738 gausslemma2dlem3
26739 lgseisenlem1
26746 lgseisenlem2
26747 lgseisenlem3
26748 lgsquadlem1
26751 lgsquadlem2
26752 2lgslem1a1
26760 2lgslem1a2
26761 2lgslem1c
26764 chebbnd1lem1
26840 chebbnd1lem2
26841 chebbnd1lem3
26842 chebbnd1
26843 chtppilimlem1
26844 chtppilimlem2
26845 chtppilim
26846 chebbnd2
26848 chto1lb
26849 chpchtlim
26850 chpo1ub
26851 dchrisum0fno1
26882 mulog2sumlem2
26906 selberglem2
26917 selberg2lem
26921 chpdifbndlem1
26924 logdivbnd
26927 pntrsumo1
26936 pntpbnd1a
26956 pntlemh
26970 pntlemr
26973 pntlemk
26977 pntlemo
26978 pnt2
26984 umgrislfupgrlem
28122 lfgrnloop
28125 lfuhgr1v0e
28251 wwlksnextwrd
28891 wwlksnextfun
28892 wwlksnextinj
28893 clwlkclwwlklem2a2
28986 konigsberg
29250 ex-fl
29440 minvecolem2
29866 minvecolem4
29871 bcsiALT
30170 opsqrlem6
31136 cdj3lem1
31425 wrdt2ind
31863 cyc2fv2
32027 sqsscirc1
32553 omssubadd
32964 signslema
33238 hgt750lem
33328 subfacval3
33847 nn0prpwlem
34847 knoppndvlem18
35045 knoppndvlem19
35046 knoppndvlem21
35048 cnndvlem1
35053 iccioo01
35848 sin2h
36118 cos2h
36119 tan2h
36120 itg2addnclem
36179 3lexlogpow5ineq2
40562 3lexlogpow5ineq4
40563 3lexlogpow5ineq3
40564 3lexlogpow2ineq1
40565 3lexlogpow2ineq2
40566 3lexlogpow5ineq5
40567 aks4d1lem1
40569 aks4d1p1p3
40576 aks4d1p1p2
40577 aks4d1p1p4
40578 aks4d1p1p6
40580 aks4d1p1p7
40581 aks4d1p1p5
40582 aks4d1p1
40583 aks4d1p2
40584 aks4d1p3
40585 aks4d1p5
40587 aks4d1p6
40588 aks4d1p7d1
40589 aks4d1p7
40590 aks4d1p8
40594 aks4d1p9
40595 2ap1caineq
40603 oexpreposd
40854 pellfundex
41256 jm2.22
41366 jm2.23
41367 imo72b2lem0
42530 sumnnodd
43961 sinaover2ne0
44199 stoweidlem14
44345 stoweidlem49
44380 stoweidlem52
44383 wallispilem4
44399 wallispi2lem2
44403 stirlinglem6
44410 stirlinglem15
44419 stirlingr
44421 dirkerval2
44425 dirkertrigeqlem3
44431 dirkercncflem4
44437 fourierdlem24
44462 fourierdlem79
44516 fourierdlem103
44540 fourierdlem104
44541 fourierdlem112
44549 fourierswlem
44561 fouriersw
44562 lighneallem4a
45890 nnoALTV
45977 nn0oALTV
45978 nn0e
45979 nneven
45980 evengpoap3
46081 nn0eo
46704 flnn0div2ge
46709 fldivexpfllog2
46741 fllog2
46744 blennngt2o2
46768 dignn0flhalf
46794 sepfsepc
47050 |