MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  2mulicn Structured version   Visualization version   GIF version

Theorem 2mulicn 11848
Description: (2 · i) ∈ ℂ. (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
2mulicn (2 · i) ∈ ℂ

Proof of Theorem 2mulicn
StepHypRef Expression
1 2cn 11700 . 2 2 ∈ ℂ
2 ax-icn 10584 . 2 i ∈ ℂ
31, 2mulcli 10636 1 (2 · i) ∈ ℂ
Colors of variables: wff setvar class
Syntax hints:  wcel 2105  (class class class)co 7145  cc 10523  ici 10527   · cmul 10530  2c2 11680
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-ext 2790  ax-1cn 10583  ax-icn 10584  ax-addcl 10585  ax-mulcl 10587
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-cleq 2811  df-clel 2890  df-2 11688
This theorem is referenced by:  imval2  14498  sinf  15465  sinneg  15487  efival  15493  sinadd  15505  dvmptim  24494  sincn  24959  sineq0  25036  sinasin  25394  efiatan2  25422  2efiatan  25423  tanatan  25424  sineq0ALT  41148
  Copyright terms: Public domain W3C validator