Theorem 2mulicn 12365

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 12220	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11085	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11139	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2113  (class class class)co 7358  ℂcc 11024  ici 11028   · cmul 11031  2c2 12200

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 2115  ax-9 2123  ax-ext 2708  ax-1cn 11084  ax-icn 11085  ax-addcl 11086  ax-mulcl 11088

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-cleq 2728  df-clel 2811  df-2 12208

This theorem is referenced by:  imval2  15074  sinf  16049  sinneg  16071  efival  16077  sinadd  16089  dvmptim  25930  sincn  26410  sineq0  26489  sinasin  26855  efiatan2  26883  2efiatan  26884  tanatan  26885  sineq0ALT  45187