Theorem 8cn 9196

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 9195	. 2 |- 8 e. RR
2	1	recni 8158	1 |- 8 e. CC

Syntax hints:   e. wcel 2200   CCcc 7997   8c8 9167

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-addrcl 8096

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  df-3 9170  df-4 9171  df-5 9172  df-6 9173  df-7 9174  df-8 9175

This theorem is referenced by:  9m1e8  9236  8p2e10  9657  8t2e16  9692  8t5e40  9695  cos2bnd  12271  2exp11  12959  2exp16  12960  lgsdir2lem1  15707  lgsdir2lem5  15711  2lgslem3a  15772  2lgslem3b  15773  2lgslem3c  15774  2lgslem3d  15775  2lgslem3a1  15776  2lgslem3b1  15777  2lgslem3c1  15778  2lgslem3d1  15779  2lgsoddprmlem1  15784  2lgsoddprmlem2  15785  2lgsoddprmlem3a  15786  2lgsoddprmlem3b  15787  2lgsoddprmlem3c  15788  2lgsoddprmlem3d  15789  ex-exp  16091