Theorem 2mulicn 12442

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 12294	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11175	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11228	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2105  (class class class)co 7412  ℂcc 11114  ici 11118   · cmul 11121  2c2 12274

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702  ax-1cn 11174  ax-icn 11175  ax-addcl 11176  ax-mulcl 11178

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1781  df-cleq 2723  df-clel 2809  df-2 12282

This theorem is referenced by:  imval2  15105  sinf  16074  sinneg  16096  efival  16102  sinadd  16114  dvmptim  25821  sincn  26295  sineq0  26372  sinasin  26734  efiatan2  26762  2efiatan  26763  tanatan  26764  sineq0ALT  44160