Theorem 2mulicn 12126

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 11978	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 10861	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 10913	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2108  (class class class)co 7255  ℂcc 10800  ici 10804   · cmul 10807  2c2 11958

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709  ax-1cn 10860  ax-icn 10861  ax-addcl 10862  ax-mulcl 10864

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1784  df-cleq 2730  df-clel 2817  df-2 11966

This theorem is referenced by:  imval2  14790  sinf  15761  sinneg  15783  efival  15789  sinadd  15801  dvmptim  25039  sincn  25508  sineq0  25585  sinasin  25944  efiatan2  25972  2efiatan  25973  tanatan  25974  sineq0ALT  42446