Theorem 2mulicn 12345

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 12200	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11065	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11119	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2111  (class class class)co 7346  ℂcc 11004  ici 11008   · cmul 11011  2c2 12180

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-1cn 11064  ax-icn 11065  ax-addcl 11066  ax-mulcl 11068

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-cleq 2723  df-clel 2806  df-2 12188

This theorem is referenced by:  imval2  15058  sinf  16033  sinneg  16055  efival  16061  sinadd  16073  dvmptim  25901  sincn  26381  sineq0  26460  sinasin  26826  efiatan2  26854  2efiatan  26855  tanatan  26856  sineq0ALT  45039