Theorem 2mulicn 12445

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 12293	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11132	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11189	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2142  (class class class)co 7396  ℂcc 11071  ici 11075   · cmul 11078  2c2 12272

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734  ax-1cn 11131  ax-icn 11132  ax-addcl 11133  ax-mulcl 11135

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1800  df-cleq 2754  df-clel 2837  df-2 12280

This theorem is referenced by:  imval2  15178  sinf  16156  sinneg  16178  efival  16184  sinadd  16196  dvmptim  26032  sincn  26507  sineq0  26589  sinasin  26954  efiatan2  26982  2efiatan  26983  tanatan  26984  sineq0ALT  45512