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| Mirrors > Home > ILE Home > Th. List > ax-icn | GIF version | ||
| Description: i is a complex number. Axiom for real and complex numbers, justified by Theorem axicn 7996. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-icn | ⊢ i ∈ ℂ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ci 7947 | . 2 class i | |
| 2 | cc 7943 | . 2 class ℂ | |
| 3 | 1, 2 | wcel 2177 | 1 wff i ∈ ℂ |
| Colors of variables: wff set class |
| This axiom is referenced by: 0cn 8084 mulrid 8089 cnegexlem2 8268 cnegex 8270 0cnALT 8282 negicn 8293 ine0 8486 ixi 8676 rimul 8678 rereim 8679 apreap 8680 cru 8695 apreim 8696 mulreim 8697 apadd1 8701 apneg 8704 aprcl 8739 aptap 8743 recextlem1 8744 recexaplem2 8745 recexap 8746 crap0 9051 cju 9054 it0e0 9278 2mulicn 9279 iap0 9280 2muliap0 9281 cnref1o 9792 irec 10806 i2 10807 i3 10808 i4 10809 iexpcyc 10811 imval 11236 imre 11237 reim 11238 crre 11243 crim 11244 remim 11246 mulreap 11250 cjreb 11252 recj 11253 reneg 11254 readd 11255 remullem 11257 imcj 11261 imneg 11262 imadd 11263 cjadd 11270 cjneg 11276 imval2 11280 rei 11285 imi 11286 cji 11288 cjreim 11289 cjreim2 11290 cjap 11292 cnrecnv 11296 rennim 11388 absi 11445 absreimsq 11453 absreim 11454 absimle 11470 climcvg1nlem 11735 sinval 12088 cosval 12089 sinf 12090 cosf 12091 tanval2ap 12099 tanval3ap 12100 resinval 12101 recosval 12102 efi4p 12103 resin4p 12104 recos4p 12105 resincl 12106 recoscl 12107 sinneg 12112 cosneg 12113 efival 12118 efmival 12119 efeul 12120 sinadd 12122 cosadd 12123 ef01bndlem 12142 sin01bnd 12143 cos01bnd 12144 absef 12156 absefib 12157 efieq1re 12158 demoivre 12159 demoivreALT 12160 igz 12772 4sqlem17 12805 cnrehmeocntop 15157 sincn 15316 coscn 15317 efhalfpi 15346 ef2kpi 15353 efper 15354 sinperlem 15355 efimpi 15366 2sqlem2 15667 qdencn 16107 |
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