Theorem 2mulicn 12468

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 12316	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11159	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11216	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2149  (class class class)co 7411  ℂcc 11098  ici 11102   · cmul 11105  2c2 12295

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-1cn 11158  ax-icn 11159  ax-addcl 11160  ax-mulcl 11162

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1807  df-cleq 2761  df-clel 2844  df-2 12303

This theorem is referenced by:  imval2  15202  sinf  16180  sinneg  16202  efival  16208  sinadd  16220  dvmptim  26098  sincn  26573  sineq0  26655  sinasin  27020  efiatan2  27048  2efiatan  27049  tanatan  27050  sineq0ALT  45571