Theorem 8cn 9157

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 9156	. 2 |- 8 e. RR
2	1	recni 8119	1 |- 8 e. CC

Syntax hints:   e. wcel 2178   CCcc 7958   8c8 9128

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189  ax-resscn 8052  ax-1re 8054  ax-addrcl 8057

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-in 3180  df-ss 3187  df-2 9130  df-3 9131  df-4 9132  df-5 9133  df-6 9134  df-7 9135  df-8 9136

This theorem is referenced by:  9m1e8  9197  8p2e10  9618  8t2e16  9653  8t5e40  9656  cos2bnd  12186  2exp11  12874  2exp16  12875  lgsdir2lem1  15620  lgsdir2lem5  15624  2lgslem3a  15685  2lgslem3b  15686  2lgslem3c  15687  2lgslem3d  15688  2lgslem3a1  15689  2lgslem3b1  15690  2lgslem3c1  15691  2lgslem3d1  15692  2lgsoddprmlem1  15697  2lgsoddprmlem2  15698  2lgsoddprmlem3a  15699  2lgsoddprmlem3b  15700  2lgsoddprmlem3c  15701  2lgsoddprmlem3d  15702  ex-exp  15863