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Mirrors > Home > ILE Home > Th. List > 2mulicn | GIF version |
Description: (2 · i) ∈ ℂ (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
2mulicn | ⊢ (2 · i) ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 9020 | . 2 ⊢ 2 ∈ ℂ | |
2 | ax-icn 7936 | . 2 ⊢ i ∈ ℂ | |
3 | 1, 2 | mulcli 7992 | 1 ⊢ (2 · i) ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 (class class class)co 5896 ℂcc 7839 ici 7843 · cmul 7846 2c2 9000 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-resscn 7933 ax-1re 7935 ax-icn 7936 ax-addrcl 7938 ax-mulcl 7939 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-in 3150 df-ss 3157 df-2 9008 |
This theorem is referenced by: 2muline0 9174 imval2 10935 sinval 11742 sinf 11744 sinneg 11766 efival 11772 sinadd 11776 sincn 14650 |
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