Theorem 2mulicn 12489

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 12341	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11214	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11268	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2108  (class class class)co 7431  ℂcc 11153  ici 11157   · cmul 11160  2c2 12321

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-1cn 11213  ax-icn 11214  ax-addcl 11215  ax-mulcl 11217

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2729  df-clel 2816  df-2 12329

This theorem is referenced by:  imval2  15190  sinf  16160  sinneg  16182  efival  16188  sinadd  16200  dvmptim  26008  sincn  26488  sineq0  26566  sinasin  26932  efiatan2  26960  2efiatan  26961  tanatan  26962  sineq0ALT  44957