Theorem 2mulicn 9477

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 9325	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 8238	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 8295	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2205  (class class class)co 6058  ℂcc 8141  ici 8145   · cmul 8148  2c2 9305

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 2216  ax-resscn 8235  ax-1re 8237  ax-icn 8238  ax-addrcl 8240  ax-mulcl 8241

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-in 3220  df-ss 3227  df-2 9313

This theorem is referenced by:  2muline0  9480  imval2  11604  sinval  12413  sinf  12415  sinneg  12437  efival  12443  sinadd  12447  sincn  15760