Theorem 2mulicn 12487

Description: (2 · i) ∈ ℂ. (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
2mulicn	⊢ (2 · i) ∈ ℂ

Proof of Theorem 2mulicn

Step	Hyp	Ref	Expression
1		2cn 12339	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11212	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11266	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2106  (class class class)co 7431  ℂcc 11151  ici 11155   · cmul 11158  2c2 12319

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-1cn 11211  ax-icn 11212  ax-addcl 11213  ax-mulcl 11215

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-cleq 2727  df-clel 2814  df-2 12327

This theorem is referenced by:  imval2  15187  sinf  16157  sinneg  16179  efival  16185  sinadd  16197  dvmptim  26023  sincn  26503  sineq0  26581  sinasin  26947  efiatan2  26975  2efiatan  26976  tanatan  26977  sineq0ALT  44935