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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 8194. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-icn | ⊢ i ∈ ℂ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ci 8145 | . 2 class i | |
| 2 | cc 8141 | . 2 class ℂ | |
| 3 | 1, 2 | wcel 2205 | 1 wff i ∈ ℂ |
| Colors of variables: wff set class |
| This axiom is referenced by: 0cn 8282 mulrid 8287 cnegexlem2 8465 cnegex 8467 0cnALT 8479 negicn 8490 ine0 8684 ixi 8874 rimul 8876 rereim 8877 apreap 8878 cru 8893 apreim 8894 mulreim 8895 apadd1 8899 apneg 8902 aprcl 8937 aptap 8941 recextlem1 8942 recexaplem2 8943 recexap 8944 crap0 9249 cju 9252 it0e0 9476 2mulicn 9477 iap0 9478 2muliap0 9479 cnref1o 10001 irec 11025 i2 11026 i3 11027 i4 11028 iexpcyc 11030 imval 11560 imre 11561 reim 11562 crre 11567 crim 11568 remim 11570 mulreap 11574 cjreb 11576 recj 11577 reneg 11578 readd 11579 remullem 11581 imcj 11585 imneg 11586 imadd 11587 cjadd 11594 cjneg 11600 imval2 11604 rei 11609 imi 11610 cji 11612 cjreim 11613 cjreim2 11614 cjap 11616 cnrecnv 11620 rennim 11712 absi 11769 absreimsq 11777 absreim 11778 absimle 11794 climcvg1nlem 12059 sinval 12413 cosval 12414 sinf 12415 cosf 12416 tanval2ap 12424 tanval3ap 12425 resinval 12426 recosval 12427 efi4p 12428 resin4p 12429 recos4p 12430 resincl 12431 recoscl 12432 sinneg 12437 cosneg 12438 efival 12443 efmival 12444 efeul 12445 sinadd 12447 cosadd 12448 ef01bndlem 12467 sin01bnd 12468 cos01bnd 12469 absef 12481 absefib 12482 efieq1re 12483 demoivre 12484 demoivreALT 12485 igz 13097 4sqlem17 13130 cnrehmeocntop 15601 sincn 15760 coscn 15761 efhalfpi 15790 ef2kpi 15797 efper 15798 sinperlem 15799 efimpi 15810 2sqlem2 16114 qdencn 16933 |
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