Theorem 8cn 9325

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 9324	. 2 |- 8 e. RR
2	1	recni 8288	1 |- 8 e. CC

Syntax hints:   e. wcel 2205   CCcc 8127   8c8 9296

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 8221  ax-1re 8223  ax-addrcl 8226

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 3219  df-ss 3226  df-2 9298  df-3 9299  df-4 9300  df-5 9301  df-6 9302  df-7 9303  df-8 9304

This theorem is referenced by:  9m1e8  9365  8p2e10  9791  8t2e16  9826  8t5e40  9829  cos2bnd  12450  2exp11  13138  2exp16  13139  lgsdir2lem1  15918  lgsdir2lem5  15922  2lgslem3a  15983  2lgslem3b  15984  2lgslem3c  15985  2lgslem3d  15986  2lgslem3a1  15987  2lgslem3b1  15988  2lgslem3c1  15989  2lgslem3d1  15990  2lgsoddprmlem1  15995  2lgsoddprmlem2  15996  2lgsoddprmlem3a  15997  2lgsoddprmlem3b  15998  2lgsoddprmlem3c  15999  2lgsoddprmlem3d  16000  ex-exp  16512