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Theorem 2mulicn 9143
Description:  ( 2  x.  _i )  e.  CC (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
2mulicn  |-  ( 2  x.  _i )  e.  CC

Proof of Theorem 2mulicn
StepHypRef Expression
1 2cn 8992 . 2  |-  2  e.  CC
2 ax-icn 7908 . 2  |-  _i  e.  CC
31, 2mulcli 7964 1  |-  ( 2  x.  _i )  e.  CC
Colors of variables: wff set class
Syntax hints:    e. wcel 2148  (class class class)co 5877   CCcc 7811   _ici 7815    x. cmul 7818   2c2 8972
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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-resscn 7905  ax-1re 7907  ax-icn 7908  ax-addrcl 7910  ax-mulcl 7911
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3137  df-ss 3144  df-2 8980
This theorem is referenced by:  2muline0  9146  imval2  10905  sinval  11712  sinf  11714  sinneg  11736  efival  11742  sinadd  11746  sincn  14229
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