Theorem 2mulicn 12377

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 12232	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11097	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11151	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2114  (class class class)co 7368  ℂcc 11036  ici 11040   · cmul 11043  2c2 12212

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-1cn 11096  ax-icn 11097  ax-addcl 11098  ax-mulcl 11100

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-cleq 2729  df-clel 2812  df-2 12220

This theorem is referenced by:  imval2  15086  sinf  16061  sinneg  16083  efival  16089  sinadd  16101  dvmptim  25942  sincn  26422  sineq0  26501  sinasin  26867  efiatan2  26895  2efiatan  26896  tanatan  26897  sineq0ALT  45292