Colors of
variables: wff
setvar class |
Syntax hints:
∈ wcel 2107 2c2 12209
ℝ+crp 12916 |
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 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-resscn 11109 ax-1cn 11110 ax-icn 11111 ax-addcl 11112 ax-addrcl 11113 ax-mulcl 11114 ax-mulrcl 11115 ax-mulcom 11116 ax-addass 11117 ax-mulass 11118 ax-distr 11119 ax-i2m1 11120 ax-1ne0 11121 ax-1rid 11122 ax-rnegex 11123 ax-rrecex 11124 ax-cnre 11125 ax-pre-lttri 11126 ax-pre-lttrn 11127 ax-pre-ltadd 11128 ax-pre-mulgt0 11129 |
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-reu 3355 df-rab 3409 df-v 3448 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-br 5107 df-opab 5169 df-mpt 5190 df-id 5532 df-po 5546 df-so 5547 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 df-er 8649 df-en 8885 df-dom 8886 df-sdom 8887 df-pnf 11192 df-mnf 11193 df-xr 11194 df-ltxr 11195 df-le 11196 df-sub 11388 df-neg 11389 df-2 12217
df-rp 12917 |
This theorem is referenced by: rphalfcl
12943 2tnp1ge0ge0
13735 flhalf
13736 fldiv4lem1div2uz2
13742 discr
14144 2swrd2eqwrdeq
14843 01sqrexlem7
15134 abstri
15216 amgm2
15255 iseralt
15570 climcndslem2
15736 climcnds
15737 efcllem
15961 oexpneg
16228 mod2eq1n2dvds
16230 oddge22np1
16232 evennn02n
16233 nn0ehalf
16261 nno
16265 nn0oddm1d2
16268 flodddiv4t2lthalf
16299 bitsfzolem
16315 bitsfzo
16316 bitsmod
16317 bitsinv1
16323 sadasslem
16351 sadeq
16353 oddprm
16683 iserodd
16708 prmreclem6
16794 prmgaplem7
16930 2expltfac
16966 psgnunilem4
19280 efgsfo
19522 efgredlemd
19527 efgredlem
19530 chfacfscmul0
22210 chfacfpmmul0
22214 psmetge0
23668 xmetge0
23700 metnrmlem3
24227 pcoass
24390 aaliou3lem1
25705 aaliou3lem2
25706 aaliou3lem3
25707 aaliou3lem8
25708 aaliou3lem5
25710 aaliou3lem6
25711 aaliou3lem7
25712 aaliou3lem9
25713 cos02pilt1
25885 cosordlem
25889 2irrexpq
26088 loglesqrt
26114 sqrt2cxp2logb9e3
26152 log2cnv
26297 log2ub
26302 log2le1
26303 birthday
26307 cxp2limlem
26328 divsqrtsumlem
26332 emcllem7
26354 emre
26358 emgt0
26359 harmonicbnd3
26360 zetacvg
26367 lgamgulmlem2
26382 lgamgulmlem3
26383 lgamucov
26390 cht2
26524 cht3
26525 chtub
26563 bclbnd
26631 bposlem6
26640 bposlem7
26641 bposlem8
26642 bposlem9
26643 gausslemma2dlem1a
26716 2lgslem3b
26748 2lgslem3c
26749 2lgslem3d
26750 2lgslem3a1
26751 2lgslem3d1
26754 chebbnd1lem2
26821 chebbnd1lem3
26822 chebbnd1
26823 chto1ub
26827 chpo1ubb
26832 rplogsumlem1
26835 selbergb
26900 selberg2b
26903 chpdifbndlem2
26905 pntrsumbnd2
26918 pntrlog2bndlem4
26931 pntrlog2bndlem5
26932 pntrlog2bndlem6
26934 pntrlog2bnd
26935 pntpbnd1a
26936 pntpbnd1
26937 pntpbnd2
26938 pntpbnd
26939 pntibndlem2
26942 pntibndlem3
26943 pntibnd
26944 pntlemr
26953 nvge0
29618 nmcexi
30971 cshw1s2
31817 sqsscirc1
32492 dya2ub
32873 dya2iocress
32877 dya2iocbrsiga
32878 dya2icobrsiga
32879 dya2icoseg
32880 sxbrsigalem2
32889 omssubadd
32903 fiblem
33001 fibp1
33004 coinflipprob
33082 signstfveq0
33192 hgt750lemd
33264 logdivsqrle
33266 hgt750lem
33267 logi
34310 unbdqndv2
34977 knoppndvlem12
34989 knoppndvlem14
34991 knoppndvlem17
34994 knoppndvlem18
34995 taupilem1
35795 taupilem2
35796 taupi
35797 poimirlem29
36110 itg2addnclem
36132 ftc1anclem7
36160 ftc1anc
36162 isbnd2
36245 lcmineqlem21
40509 lcmineqlem23
40511 3lexlogpow2ineq1
40518 dvrelog2b
40526 dvrelogpow2b
40528 aks4d1p1p2
40530 aks4d1p1p4
40531 aks4d1p1p6
40533 aks4d1p1p7
40534 aks4d1p1p5
40535 aks4d1p1
40536 aks4d1p6
40541 2np3bcnp1
40555 2ap1caineq
40556 fltne
40985 flt4lem7
41000 proot1ex
41531 sqrtcvallem2
41916 sqrtcvallem4
41918 sqrtcval
41920 oddfl
43518 sumnnodd
43878 wallispilem3
44315 wallispilem4
44316 wallispi
44318 wallispi2lem1
44319 stirlinglem2
44323 stirlinglem3
44324 stirlinglem4
44325 stirlinglem5
44326 stirlinglem6
44327 stirlinglem7
44328 stirlinglem10
44331 stirlinglem11
44332 stirlinglem13
44334 stirlinglem14
44335 stirlinglem15
44336 stirlingr
44338 dirker2re
44340 dirkerdenne0
44341 dirkerper
44344 dirkertrigeqlem1
44346 dirkertrigeqlem3
44348 dirkertrigeq
44349 dirkercncflem1
44351 dirkercncflem2
44352 dirkercncflem4
44354 fourierdlem10
44365 fourierdlem24
44379 fourierdlem62
44416 fourierdlem79
44433 fourierdlem87
44441 sqwvfoura
44476 sqwvfourb
44477 sge0ad2en
44679 ovnsubaddlem1
44818 hoiqssbllem1
44870 hoiqssbllem2
44871 hoiqssbllem3
44872 lighneallem3
45806 dfeven3
45857 dfodd4
45858 oexpnegALTV
45876 flnn0div2ge
46626 logbpw2m1
46660 fllog2
46661 blennnelnn
46669 nnpw2blen
46673 blen1b
46681 blennnt2
46682 nnolog2flm1
46683 blennngt2o2
46685 blennn0e2
46687 0dig2nn0e
46705 dignn0flhalflem1
46708 dignn0flhalflem2
46709 |