Theorem 8cn 9007

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 9006	. 2 |- 8 e. RR
2	1	recni 7971	1 |- 8 e. CC

Syntax hints:   e. wcel 2148   CCcc 7811   8c8 8978

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-resscn 7905  ax-1re 7907  ax-addrcl 7910

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3137  df-ss 3144  df-2 8980  df-3 8981  df-4 8982  df-5 8983  df-6 8984  df-7 8985  df-8 8986

This theorem is referenced by:  9m1e8  9047  8p2e10  9465  8t2e16  9500  8t5e40  9503  cos2bnd  11770  lgsdir2lem1  14514  lgsdir2lem5  14518  2lgsoddprmlem1  14538  2lgsoddprmlem2  14539  2lgsoddprmlem3a  14540  2lgsoddprmlem3b  14541  2lgsoddprmlem3c  14542  2lgsoddprmlem3d  14543  ex-exp  14564