Theorem 2mulicn 9333

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 9181	. 2 |- 2 e. CC
2		ax-icn 8094	. 2 |- _i e. CC
3	1, 2	mulcli 8151	1 |- ( 2 x. _i ) e. CC

Syntax hints:   e. wcel 2200  (class class class)co 6001   CCcc 7997   _ici 8001   x. cmul 8004   2c2 9161

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-resscn 8091  ax-1re 8093  ax-icn 8094  ax-addrcl 8096  ax-mulcl 8097

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3203  df-ss 3210  df-2 9169

This theorem is referenced by:  2muline0  9336  imval2  11405  sinval  12213  sinf  12215  sinneg  12237  efival  12243  sinadd  12247  sincn  15443