Theorem 2mulicn 12196

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 12048	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 10930	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 10982	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2106  (class class class)co 7275  ℂcc 10869  ici 10873   · cmul 10876  2c2 12028

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709  ax-1cn 10929  ax-icn 10930  ax-addcl 10931  ax-mulcl 10933

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783  df-cleq 2730  df-clel 2816  df-2 12036

This theorem is referenced by:  imval2  14862  sinf  15833  sinneg  15855  efival  15861  sinadd  15873  dvmptim  25134  sincn  25603  sineq0  25680  sinasin  26039  efiatan2  26067  2efiatan  26068  tanatan  26069  sineq0ALT  42557