Theorem 2mulicn 12406

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 12261	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11127	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11181	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2109  (class class class)co 7387  ℂcc 11066  ici 11070   · cmul 11073  2c2 12241

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 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-1cn 11126  ax-icn 11127  ax-addcl 11128  ax-mulcl 11130

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2721  df-clel 2803  df-2 12249

This theorem is referenced by:  imval2  15117  sinf  16092  sinneg  16114  efival  16120  sinadd  16132  dvmptim  25874  sincn  26354  sineq0  26433  sinasin  26799  efiatan2  26827  2efiatan  26828  tanatan  26829  sineq0ALT  44926