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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 8046. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-icn | ⊢ i ∈ ℂ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ci 7997 | . 2 class i | |
| 2 | cc 7993 | . 2 class ℂ | |
| 3 | 1, 2 | wcel 2200 | 1 wff i ∈ ℂ |
| Colors of variables: wff set class |
| This axiom is referenced by: 0cn 8134 mulrid 8139 cnegexlem2 8318 cnegex 8320 0cnALT 8332 negicn 8343 ine0 8536 ixi 8726 rimul 8728 rereim 8729 apreap 8730 cru 8745 apreim 8746 mulreim 8747 apadd1 8751 apneg 8754 aprcl 8789 aptap 8793 recextlem1 8794 recexaplem2 8795 recexap 8796 crap0 9101 cju 9104 it0e0 9328 2mulicn 9329 iap0 9330 2muliap0 9331 cnref1o 9842 irec 10856 i2 10857 i3 10858 i4 10859 iexpcyc 10861 imval 11356 imre 11357 reim 11358 crre 11363 crim 11364 remim 11366 mulreap 11370 cjreb 11372 recj 11373 reneg 11374 readd 11375 remullem 11377 imcj 11381 imneg 11382 imadd 11383 cjadd 11390 cjneg 11396 imval2 11400 rei 11405 imi 11406 cji 11408 cjreim 11409 cjreim2 11410 cjap 11412 cnrecnv 11416 rennim 11508 absi 11565 absreimsq 11573 absreim 11574 absimle 11590 climcvg1nlem 11855 sinval 12208 cosval 12209 sinf 12210 cosf 12211 tanval2ap 12219 tanval3ap 12220 resinval 12221 recosval 12222 efi4p 12223 resin4p 12224 recos4p 12225 resincl 12226 recoscl 12227 sinneg 12232 cosneg 12233 efival 12238 efmival 12239 efeul 12240 sinadd 12242 cosadd 12243 ef01bndlem 12262 sin01bnd 12263 cos01bnd 12264 absef 12276 absefib 12277 efieq1re 12278 demoivre 12279 demoivreALT 12280 igz 12892 4sqlem17 12925 cnrehmeocntop 15278 sincn 15437 coscn 15438 efhalfpi 15467 ef2kpi 15474 efper 15475 sinperlem 15476 efimpi 15487 2sqlem2 15788 qdencn 16354 |
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