Theorem 2mulicn 12435

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 12287	. 2 ⊢ 2 ∈ ℂ
2		ax-icn 11169	. 2 ⊢ i ∈ ℂ
3	1, 2	mulcli 11221	1 ⊢ (2 · i) ∈ ℂ

Syntax hints:   ∈ wcel 2107  (class class class)co 7409  ℂcc 11108  ici 11112   · cmul 11115  2c2 12267

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-1cn 11168  ax-icn 11169  ax-addcl 11170  ax-mulcl 11172

This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-cleq 2725  df-clel 2811  df-2 12275

This theorem is referenced by:  imval2  15098  sinf  16067  sinneg  16089  efival  16095  sinadd  16107  dvmptim  25487  sincn  25956  sineq0  26033  sinasin  26394  efiatan2  26422  2efiatan  26423  tanatan  26424  sineq0ALT  43746