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| Description: The number 2 is nonzero. |
| Ref | Expression |
|---|---|
| 2ne0 |
    |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 2re 7163 |
. 2
  | |
| 2 | 2pos 7173 |
. 2
 | |
| 3 | 1, 2 | gt0ne0ii 6799 |
1
|
| Colors of variables: wff set class |
| Syntax hints: wne 2017 cc0 6386 c2 7145 |
| This theorem is referenced by: 4d2e2 7211 halfpm6th 7218 halfcl 7219 rehalfcl 7220 half0 7221 2halves 7225 halfaddsub 7227 nneoi 7409 zeo 7411 zneo 7412 flhalf 7487 discrlem1 7906 nnesqi 7912 sqr2irrlem1 7974 recj 8068 imcj 8069 absmax 8149 abs3lemi 8153 faclbnd2 8198 climunii 8358 climaddlem3 8376 arisumi 8487 expcnvlem5 8492 erelem1 8581 erelem2 8582 erelem3 8583 efaddlem8 8607 efaddlem12 8611 efaddlem15 8614 efaddlem22 8621 ef4pi 8664 sincl 8696 efi4p 8700 sinneg 8707 efival 8712 sinaddi 8716 cosaddi 8717 sin01bndlem3 8735 cos01bndlem3 8737 sin02gt0 8744 znnen 8771 ioo2bl 9190 bcthlem1 9277 bcthlem21 9297 ipdirilem 9829 ubthlem8 9879 minveclem16 9905 minveclem19 9908 minveclem27 9916 minveclem35 9924 minveclem37 9926 minveclem38 9927 sinco 10016 cosco 10017 sincn 10018 coscn 10019 sinhalfpilem 10028 cospi 10031 sinhalfpip 10048 sinhalfpim 10049 coshalfpip 10050 coshalfpim 10051 sincosq1lem 10052 sincosq1sgn 10053 sincosq2sgn 10054 sincosq3sgn 10055 sincosq4sgn 10056 sinq12gt0t 10057 sincosq1eq 10059 sincos4thpi 10060 sincos6thpi 10061 abssinper 10062 coskpi 10064 sineq0re 10067 cosh111lem1 10068 norm3lem 10649 normpar2i 10656 hlimuniii 10741 projlem18 10836 mayete3i 11308 mayete3OLDi 11309 opsqrlem3 11713 opsqrlem6 11716 cntrsetlem 14999 msr3 15003 mslb1 15007 2wsms 15008 rddif 15798 absrdbnd 15799 fsumltisumi 15823 iihalf1 15872 iihalf2 15873 isbnd3 15941 heiborlem32 15986 heiborlem33 15987 rrntotbndlem1 16020 rrntotbndlem2 16021 rrntotbnd 16022 phtpycolem1 16051 phtpycolem2 16052 phtpycolem3 16053 phtpycolem4 16054 phtpycolem5 16055 phtpyco 16056 pcoval1 16074 pcoval2 16075 pcocn 16076 pco0 16077 pco1 16078 pcohtpylem1 16080 pcohtpylem2 16081 pcohtpylem3 16082 pcohtpy 16083 pcopt 16084 pcoass 16085 pcorevlem 16086 pcorev 16087 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 1304 ax-gen 1305 ax-8 1306 ax-9 1307 ax-10 1308 ax-11 1309 ax-12 1310 ax-13 1311 ax-14 1312 ax-17 1317 ax-4 1319 ax-5o 1321 ax-6o 1324 ax-9o 1481 ax-10o 1500 ax-16 1580 ax-11o 1588 ax-ext 1865 ax-rep 3428 ax-sep 3438 ax-nul 3445 ax-pow 3481 ax-pr 3524 ax-un 3790 ax-inf2 5731 |
| This theorem depends on definitions: df-bi 164 df-or 241 df-an 242 df-3or 859 df-3an 860 df-ex 1327 df-sb 1536 df-eu 1775 df-mo 1776 df-clab 1872 df-cleq 1877 df-clel 1880 df-ne 2019 df-nel 2020 df-ral 2109 df-rex 2110 df-reu 2111 df-rab 2112 df-v 2294 df-sbc 2454 df-csb 2541 df-dif 2597 df-un 2600 df-in 2603 df-ss 2605 df-pss 2607 df-nul 2876 df-if 2983 df-pw 3035 df-sn 3049 df-pr 3050 df-tp 3052 df-op 3053 df-uni 3178 df-int 3215 df-iun 3257 df-br 3339 df-opab 3396 df-tr 3412 df-eprel 3583 df-id 3586 df-po 3591 df-so 3604 df-fr 3625 df-we 3644 df-ord 3660 df-on 3661 df-lim 3662 df-suc 3663 df-om 3950 df-xp 4000 df-rel 4001 df-cnv 4002 df-co 4003 df-dm 4004 df-rn 4005 df-res 4006 df-ima 4007 df-fun 4008 df-fn 4009 df-f 4010 df-f1 4011 df-fo 4012 df-f1o 4013 df-fv 4014 df-opr 4886 df-oprab 4887 df-mpt 5006 df-1st 5020 df-2nd 5021 df-iota 5089 df-rdg 5140 df-1o 5177 df-oadd 5179 df-omul 5180 df-er 5318 df-ec 5320 df-qs 5323 df-en 5427 df-dom 5428 df-sdom 5429 df-undef 5556 df-riota 5560 df-ni 6152 df-pli 6153 df-mi 6154 df-lti 6155 df-plpq 6187 df-mpq 6188 df-enq 6189 df-nq 6190 df-plq 6191 df-mq 6192 df-rq 6193 df-ltq 6194 df-1q 6195 df-np 6238 df-1p 6239 df-plp 6240 df-mp 6241 df-ltp 6242 df-plpr 6316 df-mpr 6317 df-enr 6318 df-nr 6319 df-plr 6320 df-mr 6321 df-ltr 6322 df-0r 6323 df-1r 6324 df-m1r 6325 df-c 6392 df-0 6393 df-1 6394 df-i 6395 df-r 6396 df-plus 6397 df-mul 6398 df-lt 6399 df-sub 6511 df-neg 6513 df-pnf 6654 df-mnf 6655 df-xr 6656 df-ltxr 6657 df-le 6658 df-2 7154 |