Theorem 8cn 9124

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 9123	. 2 |- 8 e. RR
2	1	recni 8086	1 |- 8 e. CC

Syntax hints:   e. wcel 2176   CCcc 7925   8c8 9095

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187  ax-resscn 8019  ax-1re 8021  ax-addrcl 8024

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-in 3172  df-ss 3179  df-2 9097  df-3 9098  df-4 9099  df-5 9100  df-6 9101  df-7 9102  df-8 9103

This theorem is referenced by:  9m1e8  9164  8p2e10  9585  8t2e16  9620  8t5e40  9623  cos2bnd  12104  2exp11  12792  2exp16  12793  lgsdir2lem1  15538  lgsdir2lem5  15542  2lgslem3a  15603  2lgslem3b  15604  2lgslem3c  15605  2lgslem3d  15606  2lgslem3a1  15607  2lgslem3b1  15608  2lgslem3c1  15609  2lgslem3d1  15610  2lgsoddprmlem1  15615  2lgsoddprmlem2  15616  2lgsoddprmlem3a  15617  2lgsoddprmlem3b  15618  2lgsoddprmlem3c  15619  2lgsoddprmlem3d  15620  ex-exp  15700