Theorem 2mulicn 9460

Description: (2 · i) ∈ ℂ (common case). (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 9308	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 8222	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 8279	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2203  (class class class)co 6050  ℂcc 8125  ici 8129   · cmul 8132  2c2 9288

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214  ax-resscn 8219  ax-1re 8221  ax-icn 8222  ax-addrcl 8224  ax-mulcl 8225

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-in 3217  df-ss 3224  df-2 9296

This theorem is referenced by:  2muline0  9463  imval2  11579  sinval  12388  sinf  12390  sinneg  12412  efival  12418  sinadd  12422  sincn  15634