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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 8082. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-icn | ⊢ i ∈ ℂ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ci 8033 | . 2 class i | |
| 2 | cc 8029 | . 2 class ℂ | |
| 3 | 1, 2 | wcel 2202 | 1 wff i ∈ ℂ |
| Colors of variables: wff set class |
| This axiom is referenced by: 0cn 8170 mulrid 8175 cnegexlem2 8354 cnegex 8356 0cnALT 8368 negicn 8379 ine0 8572 ixi 8762 rimul 8764 rereim 8765 apreap 8766 cru 8781 apreim 8782 mulreim 8783 apadd1 8787 apneg 8790 aprcl 8825 aptap 8829 recextlem1 8830 recexaplem2 8831 recexap 8832 crap0 9137 cju 9140 it0e0 9364 2mulicn 9365 iap0 9366 2muliap0 9367 cnref1o 9884 irec 10900 i2 10901 i3 10902 i4 10903 iexpcyc 10905 imval 11410 imre 11411 reim 11412 crre 11417 crim 11418 remim 11420 mulreap 11424 cjreb 11426 recj 11427 reneg 11428 readd 11429 remullem 11431 imcj 11435 imneg 11436 imadd 11437 cjadd 11444 cjneg 11450 imval2 11454 rei 11459 imi 11460 cji 11462 cjreim 11463 cjreim2 11464 cjap 11466 cnrecnv 11470 rennim 11562 absi 11619 absreimsq 11627 absreim 11628 absimle 11644 climcvg1nlem 11909 sinval 12262 cosval 12263 sinf 12264 cosf 12265 tanval2ap 12273 tanval3ap 12274 resinval 12275 recosval 12276 efi4p 12277 resin4p 12278 recos4p 12279 resincl 12280 recoscl 12281 sinneg 12286 cosneg 12287 efival 12292 efmival 12293 efeul 12294 sinadd 12296 cosadd 12297 ef01bndlem 12316 sin01bnd 12317 cos01bnd 12318 absef 12330 absefib 12331 efieq1re 12332 demoivre 12333 demoivreALT 12334 igz 12946 4sqlem17 12979 cnrehmeocntop 15333 sincn 15492 coscn 15493 efhalfpi 15522 ef2kpi 15529 efper 15530 sinperlem 15531 efimpi 15542 2sqlem2 15843 qdencn 16631 |
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