Theorem 8cn 9323

Description: The number 8 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
8cn	⊢ 8 ∈ ℂ

Proof of Theorem 8cn

Step	Hyp	Ref	Expression
1		8re 9322	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8286	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2203  ℂcc 8125  8c8 9294

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 2214  ax-resscn 8219  ax-1re 8221  ax-addrcl 8224

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-in 3217  df-ss 3224  df-2 9296  df-3 9297  df-4 9298  df-5 9299  df-6 9300  df-7 9301  df-8 9302

This theorem is referenced by:  9m1e8  9363  8p2e10  9788  8t2e16  9823  8t5e40  9826  cos2bnd  12446  2exp11  13134  2exp16  13135  lgsdir2lem1  15901  lgsdir2lem5  15905  2lgslem3a  15966  2lgslem3b  15967  2lgslem3c  15968  2lgslem3d  15969  2lgslem3a1  15970  2lgslem3b1  15971  2lgslem3c1  15972  2lgslem3d1  15973  2lgsoddprmlem1  15978  2lgsoddprmlem2  15979  2lgsoddprmlem3a  15980  2lgsoddprmlem3b  15981  2lgsoddprmlem3c  15982  2lgsoddprmlem3d  15983  ex-exp  16495