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Mirrors > Home > MPE Home > Th. List > halfcn | Structured version Visualization version GIF version |
Description: One-half is a complex number. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
halfcn | ⊢ (1 / 2) ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 11700 | . 2 ⊢ 2 ∈ ℂ | |
2 | 2ne0 11729 | . 2 ⊢ 2 ≠ 0 | |
3 | 1, 2 | reccli 11358 | 1 ⊢ (1 / 2) ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2105 (class class class)co 7145 ℂcc 10523 1c1 10526 / cdiv 11285 2c2 11680 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pow 5257 ax-pr 5320 ax-un 7450 ax-resscn 10582 ax-1cn 10583 ax-icn 10584 ax-addcl 10585 ax-addrcl 10586 ax-mulcl 10587 ax-mulrcl 10588 ax-mulcom 10589 ax-addass 10590 ax-mulass 10591 ax-distr 10592 ax-i2m1 10593 ax-1ne0 10594 ax-1rid 10595 ax-rnegex 10596 ax-rrecex 10597 ax-cnre 10598 ax-pre-lttri 10599 ax-pre-lttrn 10600 ax-pre-ltadd 10601 ax-pre-mulgt0 10602 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3or 1080 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ne 3014 df-nel 3121 df-ral 3140 df-rex 3141 df-reu 3142 df-rmo 3143 df-rab 3144 df-v 3494 df-sbc 3770 df-csb 3881 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-pw 4537 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-opab 5120 df-mpt 5138 df-id 5453 df-po 5467 df-so 5468 df-xp 5554 df-rel 5555 df-cnv 5556 df-co 5557 df-dm 5558 df-rn 5559 df-res 5560 df-ima 5561 df-iota 6307 df-fun 6350 df-fn 6351 df-f 6352 df-f1 6353 df-fo 6354 df-f1o 6355 df-fv 6356 df-riota 7103 df-ov 7148 df-oprab 7149 df-mpo 7150 df-er 8278 df-en 8498 df-dom 8499 df-sdom 8500 df-pnf 10665 df-mnf 10666 df-xr 10667 df-ltxr 10668 df-le 10669 df-sub 10860 df-neg 10861 df-div 11286 df-2 11688 |
This theorem is referenced by: halfpm6th 11846 rddif 14688 geo2sum 15217 geo2lim 15219 geoihalfsum 15226 bpoly1 15393 bpoly2 15399 bpoly3 15400 efcllem 15419 ege2le3 15431 efival 15493 flodddiv4 15752 pcoass 23555 iscmet3lem3 23820 mbfi1fseqlem6 24248 dvmptre 24493 aaliou3lem2 24859 aaliou3lem3 24860 sincos4thpi 25026 cxpsqrt 25213 dvsqrt 25250 dvcnsqrt 25252 resqrtcn 25257 ang180lem3 25316 heron 25343 efiatan 25417 efiatan2 25422 gausslemma2dlem1a 25868 ipdirilem 28533 mayete3i 29432 opsqrlem6 29849 dnibndlem3 33716 dnibndlem6 33719 cntotbnd 34955 stirlinglem1 42236 dirkerper 42258 dirkertrigeqlem3 42262 dirkeritg 42264 dirkercncflem2 42266 fourierdlem18 42287 fourierdlem57 42325 fourierdlem58 42326 fourierdlem62 42330 fourierdlem103 42371 fourierdlem104 42372 0nodd 43954 |
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