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Mirrors > Home > ILE Home > Th. List > picn | Unicode version |
Description: ![]() |
Ref | Expression |
---|---|
picn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pire 13867 |
. 2
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2 | 1 | recni 7957 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-coll 4115 ax-sep 4118 ax-nul 4126 ax-pow 4171 ax-pr 4206 ax-un 4430 ax-setind 4533 ax-iinf 4584 ax-cnex 7890 ax-resscn 7891 ax-1cn 7892 ax-1re 7893 ax-icn 7894 ax-addcl 7895 ax-addrcl 7896 ax-mulcl 7897 ax-mulrcl 7898 ax-addcom 7899 ax-mulcom 7900 ax-addass 7901 ax-mulass 7902 ax-distr 7903 ax-i2m1 7904 ax-0lt1 7905 ax-1rid 7906 ax-0id 7907 ax-rnegex 7908 ax-precex 7909 ax-cnre 7910 ax-pre-ltirr 7911 ax-pre-ltwlin 7912 ax-pre-lttrn 7913 ax-pre-apti 7914 ax-pre-ltadd 7915 ax-pre-mulgt0 7916 ax-pre-mulext 7917 ax-arch 7918 ax-caucvg 7919 ax-pre-suploc 7920 ax-addf 7921 ax-mulf 7922 |
This theorem depends on definitions: df-bi 117 df-stab 831 df-dc 835 df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-reu 2462 df-rmo 2463 df-rab 2464 df-v 2739 df-sbc 2963 df-csb 3058 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-if 3535 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-int 3843 df-iun 3886 df-disj 3978 df-br 4001 df-opab 4062 df-mpt 4063 df-tr 4099 df-id 4290 df-po 4293 df-iso 4294 df-iord 4363 df-on 4365 df-ilim 4366 df-suc 4368 df-iom 4587 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-rn 4634 df-res 4635 df-ima 4636 df-iota 5174 df-fun 5214 df-fn 5215 df-f 5216 df-f1 5217 df-fo 5218 df-f1o 5219 df-fv 5220 df-isom 5221 df-riota 5825 df-ov 5872 df-oprab 5873 df-mpo 5874 df-of 6077 df-1st 6135 df-2nd 6136 df-recs 6300 df-irdg 6365 df-frec 6386 df-1o 6411 df-oadd 6415 df-er 6529 df-map 6644 df-pm 6645 df-en 6735 df-dom 6736 df-fin 6737 df-sup 6977 df-inf 6978 df-pnf 7981 df-mnf 7982 df-xr 7983 df-ltxr 7984 df-le 7985 df-sub 8117 df-neg 8118 df-reap 8519 df-ap 8526 df-div 8616 df-inn 8906 df-2 8964 df-3 8965 df-4 8966 df-5 8967 df-6 8968 df-7 8969 df-8 8970 df-9 8971 df-n0 9163 df-z 9240 df-uz 9515 df-q 9606 df-rp 9638 df-xneg 9756 df-xadd 9757 df-ioo 9876 df-ioc 9877 df-ico 9878 df-icc 9879 df-fz 9993 df-fzo 10126 df-seqfrec 10429 df-exp 10503 df-fac 10687 df-bc 10709 df-ihash 10737 df-shft 10805 df-cj 10832 df-re 10833 df-im 10834 df-rsqrt 10988 df-abs 10989 df-clim 11268 df-sumdc 11343 df-ef 11637 df-sin 11639 df-cos 11640 df-pi 11642 df-rest 12635 df-topgen 12654 df-psmet 13147 df-xmet 13148 df-met 13149 df-bl 13150 df-mopn 13151 df-top 13156 df-topon 13169 df-bases 13201 df-ntr 13256 df-cn 13348 df-cnp 13349 df-tx 13413 df-cncf 13718 df-limced 13785 df-dvap 13786 |
This theorem is referenced by: negpicn 13871 pidiv2halves 13876 efhalfpi 13880 cospi 13881 efipi 13882 sin2pi 13884 cos2pi 13885 ef2pi 13886 ef2kpi 13887 efper 13888 sinperlem 13889 sin2kpi 13892 cos2kpi 13893 sin2pim 13894 cos2pim 13895 sinmpi 13896 cosmpi 13897 sinppi 13898 cosppi 13899 efimpi 13900 ptolemy 13905 sinq12gt0 13911 sinq34lt0t 13912 cosq14gt0 13913 cosq23lt0 13914 coseq0q4123 13915 sincos6thpi 13923 sincos3rdpi 13924 abssinper 13927 sinkpi 13928 coskpi 13929 cosq34lt1 13931 |
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