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Mirrors > Home > MPE Home > Th. List > 2mulicn | Structured version Visualization version 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 11091 | . 2 ⊢ 2 ∈ ℂ | |
2 | ax-icn 9995 | . 2 ⊢ i ∈ ℂ | |
3 | 1, 2 | mulcli 10045 | 1 ⊢ (2 · i) ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1990 (class class class)co 6650 ℂcc 9934 ici 9938 · cmul 9941 2c2 11070 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-i2m1 10004 ax-1ne0 10005 ax-rrecex 10008 ax-cnre 10009 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 df-2 11079 |
This theorem is referenced by: imval2 13891 sinf 14854 sinneg 14876 efival 14882 sinadd 14894 dvmptim 23733 sincn 24198 sineq0 24273 sinasin 24616 efiatan2 24644 2efiatan 24645 tanatan 24646 sineq0ALT 39173 |
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