Theorem 2mulicn 11910

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 11762	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 10647	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 10699	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2111  (class class class)co 7156  ℂcc 10586  ici 10590   · cmul 10593  2c2 11742

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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729  ax-1cn 10646  ax-icn 10647  ax-addcl 10648  ax-mulcl 10650

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-cleq 2750  df-clel 2830  df-2 11750

This theorem is referenced by:  imval2  14571  sinf  15538  sinneg  15560  efival  15566  sinadd  15578  dvmptim  24683  sincn  25152  sineq0  25229  sinasin  25588  efiatan2  25616  2efiatan  25617  tanatan  25618  sineq0ALT  42061