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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 8223. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-icn | ⊢ i ∈ ℂ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ci 8174 | . 2 class i | |
| 2 | cc 8170 | . 2 class ℂ | |
| 3 | 1, 2 | wcel 2209 | 1 wff i ∈ ℂ |
| Colors of variables: wff set class |
| This axiom is referenced by: 0cn 8311 mulrid 8316 cnegexlem2 8495 cnegex 8497 0cnALT 8509 negicn 8520 ine0 8714 ixi 8904 rimul 8906 rereim 8907 apreap 8908 cru 8923 apreim 8924 mulreim 8925 apadd1 8929 apneg 8932 aprcl 8967 aptap 8971 recextlem1 8972 recexaplem2 8973 recexap 8974 crap0 9281 cju 9284 it0e0 9508 2mulicn 9509 iap0 9510 2muliap0 9511 cnref1o 10033 irec 11057 i2 11058 i3 11059 i4 11060 iexpcyc 11062 imval 11596 imre 11597 reim 11598 crre 11603 crim 11604 remim 11606 mulreap 11610 cjreb 11612 recj 11613 reneg 11614 readd 11615 remullem 11617 imcj 11621 imneg 11622 imadd 11623 cjadd 11630 cjneg 11636 imval2 11640 sq01 11641 rei 11646 imi 11647 cji 11649 cjreim 11650 cjreim2 11651 cjap 11653 cnrecnv 11657 rennim 11749 absi 11806 absreimsq 11814 absreim 11815 absimle 11831 climcvg1nlem 12096 sinval 12450 cosval 12451 sinf 12452 cosf 12453 tanval2ap 12461 tanval3ap 12462 resinval 12463 recosval 12464 efi4p 12465 resin4p 12466 recos4p 12467 resincl 12468 recoscl 12469 sinneg 12474 cosneg 12475 efival 12480 efmival 12481 efeul 12482 sinadd 12484 cosadd 12485 ef01bndlem 12504 sin01bnd 12505 cos01bnd 12506 absef 12518 absefib 12519 efieq1re 12520 demoivre 12521 demoivreALT 12522 igz 13134 4sqlem17 13167 cnrehmeocntop 15637 sincn 15796 coscn 15797 efhalfpi 15826 ef2kpi 15833 efper 15834 sinperlem 15835 efimpi 15846 2sqlem2 16151 qdencn 16980 |
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