Theorem 2mulicn 12465

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 12315	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11188	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11242	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2108  (class class class)co 7405  ℂcc 11127  ici 11131   · cmul 11134  2c2 12295

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 2707  ax-1cn 11187  ax-icn 11188  ax-addcl 11189  ax-mulcl 11191

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2727  df-clel 2809  df-2 12303

This theorem is referenced by:  imval2  15170  sinf  16142  sinneg  16164  efival  16170  sinadd  16182  dvmptim  25926  sincn  26406  sineq0  26485  sinasin  26851  efiatan2  26879  2efiatan  26880  tanatan  26881  sineq0ALT  44961