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| Mirrors > Home > MPE Home > Th. List > 2mulicn | Structured version Visualization version GIF version | ||
| Description: (2 · i) ∈ ℂ. (Contributed by David A. Wheeler, 8-Dec-2018.) |
| Ref | Expression |
|---|---|
| 2mulicn | ⊢ (2 · i) ∈ ℂ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 2cn 12341 | . 2 ⊢ 2 ∈ ℂ | |
| 2 | ax-icn 11214 | . 2 ⊢ i ∈ ℂ | |
| 3 | 1, 2 | mulcli 11268 | 1 ⊢ (2 · i) ∈ ℂ |
| Colors of variables: wff setvar class |
| Syntax hints: ∈ wcel 2108 (class class class)co 7431 ℂcc 11153 ici 11157 · cmul 11160 2c2 12321 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-1cn 11213 ax-icn 11214 ax-addcl 11215 ax-mulcl 11217 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-cleq 2729 df-clel 2816 df-2 12329 |
| This theorem is referenced by: imval2 15190 sinf 16160 sinneg 16182 efival 16188 sinadd 16200 dvmptim 26008 sincn 26488 sineq0 26566 sinasin 26932 efiatan2 26960 2efiatan 26961 tanatan 26962 sineq0ALT 44957 |
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