Theorem 8cn 9229

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 9228	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8191	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2202  ℂcc 8030  8c8 9200

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 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-resscn 8124  ax-1re 8126  ax-addrcl 8129

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3206  df-ss 3213  df-2 9202  df-3 9203  df-4 9204  df-5 9205  df-6 9206  df-7 9207  df-8 9208

This theorem is referenced by:  9m1e8  9269  8p2e10  9690  8t2e16  9725  8t5e40  9728  cos2bnd  12339  2exp11  13027  2exp16  13028  lgsdir2lem1  15776  lgsdir2lem5  15780  2lgslem3a  15841  2lgslem3b  15842  2lgslem3c  15843  2lgslem3d  15844  2lgslem3a1  15845  2lgslem3b1  15846  2lgslem3c1  15847  2lgslem3d1  15848  2lgsoddprmlem1  15853  2lgsoddprmlem2  15854  2lgsoddprmlem3a  15855  2lgsoddprmlem3b  15856  2lgsoddprmlem3c  15857  2lgsoddprmlem3d  15858  ex-exp  16370