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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 8180. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-icn | ⊢ i ∈ ℂ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ci 8131 | . 2 class i | |
| 2 | cc 8127 | . 2 class ℂ | |
| 3 | 1, 2 | wcel 2205 | 1 wff i ∈ ℂ |
| Colors of variables: wff set class |
| This axiom is referenced by: 0cn 8268 mulrid 8273 cnegexlem2 8451 cnegex 8453 0cnALT 8465 negicn 8476 ine0 8669 ixi 8859 rimul 8861 rereim 8862 apreap 8863 cru 8878 apreim 8879 mulreim 8880 apadd1 8884 apneg 8887 aprcl 8922 aptap 8926 recextlem1 8927 recexaplem2 8928 recexap 8929 crap0 9234 cju 9237 it0e0 9461 2mulicn 9462 iap0 9463 2muliap0 9464 cnref1o 9986 irec 11005 i2 11006 i3 11007 i4 11008 iexpcyc 11010 imval 11539 imre 11540 reim 11541 crre 11546 crim 11547 remim 11549 mulreap 11553 cjreb 11555 recj 11556 reneg 11557 readd 11558 remullem 11560 imcj 11564 imneg 11565 imadd 11566 cjadd 11573 cjneg 11579 imval2 11583 rei 11588 imi 11589 cji 11591 cjreim 11592 cjreim2 11593 cjap 11595 cnrecnv 11599 rennim 11691 absi 11748 absreimsq 11756 absreim 11757 absimle 11773 climcvg1nlem 12038 sinval 12392 cosval 12393 sinf 12394 cosf 12395 tanval2ap 12403 tanval3ap 12404 resinval 12405 recosval 12406 efi4p 12407 resin4p 12408 recos4p 12409 resincl 12410 recoscl 12411 sinneg 12416 cosneg 12417 efival 12422 efmival 12423 efeul 12424 sinadd 12426 cosadd 12427 ef01bndlem 12446 sin01bnd 12447 cos01bnd 12448 absef 12460 absefib 12461 efieq1re 12462 demoivre 12463 demoivreALT 12464 igz 13076 4sqlem17 13109 cnrehmeocntop 15492 sincn 15651 coscn 15652 efhalfpi 15681 ef2kpi 15688 efper 15689 sinperlem 15690 efimpi 15701 2sqlem2 16005 qdencn 16824 |
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