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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 8061. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-icn | ⊢ i ∈ ℂ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ci 8012 | . 2 class i | |
| 2 | cc 8008 | . 2 class ℂ | |
| 3 | 1, 2 | wcel 2200 | 1 wff i ∈ ℂ |
| Colors of variables: wff set class |
| This axiom is referenced by: 0cn 8149 mulrid 8154 cnegexlem2 8333 cnegex 8335 0cnALT 8347 negicn 8358 ine0 8551 ixi 8741 rimul 8743 rereim 8744 apreap 8745 cru 8760 apreim 8761 mulreim 8762 apadd1 8766 apneg 8769 aprcl 8804 aptap 8808 recextlem1 8809 recexaplem2 8810 recexap 8811 crap0 9116 cju 9119 it0e0 9343 2mulicn 9344 iap0 9345 2muliap0 9346 cnref1o 9858 irec 10873 i2 10874 i3 10875 i4 10876 iexpcyc 10878 imval 11376 imre 11377 reim 11378 crre 11383 crim 11384 remim 11386 mulreap 11390 cjreb 11392 recj 11393 reneg 11394 readd 11395 remullem 11397 imcj 11401 imneg 11402 imadd 11403 cjadd 11410 cjneg 11416 imval2 11420 rei 11425 imi 11426 cji 11428 cjreim 11429 cjreim2 11430 cjap 11432 cnrecnv 11436 rennim 11528 absi 11585 absreimsq 11593 absreim 11594 absimle 11610 climcvg1nlem 11875 sinval 12228 cosval 12229 sinf 12230 cosf 12231 tanval2ap 12239 tanval3ap 12240 resinval 12241 recosval 12242 efi4p 12243 resin4p 12244 recos4p 12245 resincl 12246 recoscl 12247 sinneg 12252 cosneg 12253 efival 12258 efmival 12259 efeul 12260 sinadd 12262 cosadd 12263 ef01bndlem 12282 sin01bnd 12283 cos01bnd 12284 absef 12296 absefib 12297 efieq1re 12298 demoivre 12299 demoivreALT 12300 igz 12912 4sqlem17 12945 cnrehmeocntop 15299 sincn 15458 coscn 15459 efhalfpi 15488 ef2kpi 15495 efper 15496 sinperlem 15497 efimpi 15508 2sqlem2 15809 qdencn 16455 |
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