Theorem 2mulicn 12413

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 12268	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11134	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11188	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2109  (class class class)co 7390  ℂcc 11073  ici 11077   · cmul 11080  2c2 12248

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 2702  ax-1cn 11133  ax-icn 11134  ax-addcl 11135  ax-mulcl 11137

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2722  df-clel 2804  df-2 12256

This theorem is referenced by:  imval2  15124  sinf  16099  sinneg  16121  efival  16127  sinadd  16139  dvmptim  25881  sincn  26361  sineq0  26440  sinasin  26806  efiatan2  26834  2efiatan  26835  tanatan  26836  sineq0ALT  44933