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Mirrors > Home > MPE Home > Th. List > halfcn | Structured version Visualization version GIF version |
Description: One-half is complex. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
halfcn | ⊢ (1 / 2) ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 11129 | . 2 ⊢ 2 ∈ ℂ | |
2 | 2ne0 11151 | . 2 ⊢ 2 ≠ 0 | |
3 | 1, 2 | reccli 10793 | 1 ⊢ (1 / 2) ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2030 (class class class)co 6690 ℂcc 9972 1c1 9975 / cdiv 10722 2c2 11108 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-8 2032 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 ax-sep 4814 ax-nul 4822 ax-pow 4873 ax-pr 4936 ax-un 6991 ax-resscn 10031 ax-1cn 10032 ax-icn 10033 ax-addcl 10034 ax-addrcl 10035 ax-mulcl 10036 ax-mulrcl 10037 ax-mulcom 10038 ax-addass 10039 ax-mulass 10040 ax-distr 10041 ax-i2m1 10042 ax-1ne0 10043 ax-1rid 10044 ax-rnegex 10045 ax-rrecex 10046 ax-cnre 10047 ax-pre-lttri 10048 ax-pre-lttrn 10049 ax-pre-ltadd 10050 ax-pre-mulgt0 10051 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3or 1055 df-3an 1056 df-tru 1526 df-ex 1745 df-nf 1750 df-sb 1938 df-eu 2502 df-mo 2503 df-clab 2638 df-cleq 2644 df-clel 2647 df-nfc 2782 df-ne 2824 df-nel 2927 df-ral 2946 df-rex 2947 df-reu 2948 df-rmo 2949 df-rab 2950 df-v 3233 df-sbc 3469 df-csb 3567 df-dif 3610 df-un 3612 df-in 3614 df-ss 3621 df-nul 3949 df-if 4120 df-pw 4193 df-sn 4211 df-pr 4213 df-op 4217 df-uni 4469 df-br 4686 df-opab 4746 df-mpt 4763 df-id 5053 df-po 5064 df-so 5065 df-xp 5149 df-rel 5150 df-cnv 5151 df-co 5152 df-dm 5153 df-rn 5154 df-res 5155 df-ima 5156 df-iota 5889 df-fun 5928 df-fn 5929 df-f 5930 df-f1 5931 df-fo 5932 df-f1o 5933 df-fv 5934 df-riota 6651 df-ov 6693 df-oprab 6694 df-mpt2 6695 df-er 7787 df-en 7998 df-dom 7999 df-sdom 8000 df-pnf 10114 df-mnf 10115 df-xr 10116 df-ltxr 10117 df-le 10118 df-sub 10306 df-neg 10307 df-div 10723 df-2 11117 |
This theorem is referenced by: halfpm6th 11291 rddif 14124 geo2sum 14648 geo2lim 14650 geoihalfsum 14658 bpoly1 14826 bpoly2 14832 bpoly3 14833 efcllem 14852 ege2le3 14864 efival 14926 flodddiv4 15184 pcoass 22870 iscmet3lem3 23134 mbfi1fseqlem6 23532 dvmptre 23777 aaliou3lem2 24143 aaliou3lem3 24144 sincos4thpi 24310 cxpsqrt 24494 dvsqrt 24528 dvcnsqrt 24530 resqrtcn 24535 ang180lem3 24586 heron 24610 efiatan 24684 efiatan2 24689 gausslemma2dlem1a 25135 ipdirilem 27812 mayete3i 28715 opsqrlem6 29132 dnibndlem3 32595 dnibndlem6 32598 cntotbnd 33725 stirlinglem1 40609 dirkerper 40631 dirkertrigeqlem3 40635 dirkeritg 40637 dirkercncflem2 40639 fourierdlem18 40660 fourierdlem57 40698 fourierdlem58 40699 fourierdlem62 40703 fourierdlem103 40744 fourierdlem104 40745 0nodd 42135 |
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