ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  2mulicn GIF version

Theorem 2mulicn 9171
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
StepHypRef Expression
1 2cn 9020 . 2 2 ∈ ℂ
2 ax-icn 7936 . 2 i ∈ ℂ
31, 2mulcli 7992 1 (2 · i) ∈ ℂ
Colors of variables: wff set class
Syntax hints:  wcel 2160  (class class class)co 5896  cc 7839  ici 7843   · cmul 7846  2c2 9000
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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-resscn 7933  ax-1re 7935  ax-icn 7936  ax-addrcl 7938  ax-mulcl 7939
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-in 3150  df-ss 3157  df-2 9008
This theorem is referenced by:  2muline0  9174  imval2  10935  sinval  11742  sinf  11744  sinneg  11766  efival  11772  sinadd  11776  sincn  14650
  Copyright terms: Public domain W3C validator