Theorem 2mulicn 12392

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 12247	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11088	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11143	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2119  (class class class)co 7356  ℂcc 11027  ici 11031   · cmul 11034  2c2 12227

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711  ax-1cn 11087  ax-icn 11088  ax-addcl 11089  ax-mulcl 11091

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-cleq 2731  df-clel 2814  df-2 12235

This theorem is referenced by:  imval2  15104  sinf  16082  sinneg  16104  efival  16110  sinadd  16122  dvmptim  25955  sincn  26427  sineq0  26506  sinasin  26871  efiatan2  26899  2efiatan  26900  tanatan  26901  sineq0ALT  45380