Theorem 2mulicn 12516

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 12368	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11243	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11297	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2108  (class class class)co 7448  ℂcc 11182  ici 11186   · cmul 11189  2c2 12348

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-1cn 11242  ax-icn 11243  ax-addcl 11244  ax-mulcl 11246

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1778  df-cleq 2732  df-clel 2819  df-2 12356

This theorem is referenced by:  imval2  15200  sinf  16172  sinneg  16194  efival  16200  sinadd  16212  dvmptim  26028  sincn  26506  sineq0  26584  sinasin  26950  efiatan2  26978  2efiatan  26979  tanatan  26980  sineq0ALT  44908