Theorem 8cn 9340

Description: The number 8 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
8cn	|- 8 e. CC

Proof of Theorem 8cn

Step	Hyp	Ref	Expression
1		8re 9339	. 2 |- 8 e. RR
2	1	recni 8302	1 |- 8 e. CC

Syntax hints:   e. wcel 2205   CCcc 8141   8c8 9311

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 2216  ax-resscn 8235  ax-1re 8237  ax-addrcl 8240

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-in 3220  df-ss 3227  df-2 9313  df-3 9314  df-4 9315  df-5 9316  df-6 9317  df-7 9318  df-8 9319

This theorem is referenced by:  9m1e8  9380  8p2e10  9806  8t2e16  9841  8t5e40  9844  cos2bnd  12471  2exp11  13159  2exp16  13160  lgsdir2lem1  16027  lgsdir2lem5  16031  2lgslem3a  16092  2lgslem3b  16093  2lgslem3c  16094  2lgslem3d  16095  2lgslem3a1  16096  2lgslem3b1  16097  2lgslem3c1  16098  2lgslem3d1  16099  2lgsoddprmlem1  16104  2lgsoddprmlem2  16105  2lgsoddprmlem3a  16106  2lgsoddprmlem3b  16107  2lgsoddprmlem3c  16108  2lgsoddprmlem3d  16109  ex-exp  16621