Theorem 2mulicn 12385

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 12237	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11119	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11171	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2106  (class class class)co 7362  ℂcc 11058  ici 11062   · cmul 11065  2c2 12217

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702  ax-1cn 11118  ax-icn 11119  ax-addcl 11120  ax-mulcl 11122

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1782  df-cleq 2723  df-clel 2809  df-2 12225

This theorem is referenced by:  imval2  15048  sinf  16017  sinneg  16039  efival  16045  sinadd  16057  dvmptim  25371  sincn  25840  sineq0  25917  sinasin  26276  efiatan2  26304  2efiatan  26305  tanatan  26306  sineq0ALT  43341