Theorem 2mulicn 12382

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 12237	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11103	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11157	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2109  (class class class)co 7369  ℂcc 11042  ici 11046   · cmul 11049  2c2 12217

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 11102  ax-icn 11103  ax-addcl 11104  ax-mulcl 11106

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2721  df-clel 2803  df-2 12225

This theorem is referenced by:  imval2  15093  sinf  16068  sinneg  16090  efival  16096  sinadd  16108  dvmptim  25850  sincn  26330  sineq0  26409  sinasin  26775  efiatan2  26803  2efiatan  26804  tanatan  26805  sineq0ALT  44899