Theorem 2mulicn 9459

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

Step	Hyp	Ref	Expression
1		2cn 9307	. 2 |- 2 e. CC
2		ax-icn 8221	. 2 |- _i e. CC
3	1, 2	mulcli 8278	1 |- ( 2 x. _i ) e. CC

Syntax hints:   e. wcel 2203  (class class class)co 6049   CCcc 8124   _ici 8128   x. cmul 8131   2c2 9287

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214  ax-resscn 8218  ax-1re 8220  ax-icn 8221  ax-addrcl 8223  ax-mulcl 8224

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-in 3216  df-ss 3223  df-2 9295

This theorem is referenced by:  2muline0  9462  imval2  11575  sinval  12384  sinf  12386  sinneg  12408  efival  12414  sinadd  12418  sincn  15626