Theorem 8cn 9228

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 9227	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8190	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2202  ℂcc 8029  8c8 9199

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 8123  ax-1re 8125  ax-addrcl 8128

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 9201  df-3 9202  df-4 9203  df-5 9204  df-6 9205  df-7 9206  df-8 9207

This theorem is referenced by:  9m1e8  9268  8p2e10  9689  8t2e16  9724  8t5e40  9727  cos2bnd  12320  2exp11  13008  2exp16  13009  lgsdir2lem1  15756  lgsdir2lem5  15760  2lgslem3a  15821  2lgslem3b  15822  2lgslem3c  15823  2lgslem3d  15824  2lgslem3a1  15825  2lgslem3b1  15826  2lgslem3c1  15827  2lgslem3d1  15828  2lgsoddprmlem1  15833  2lgsoddprmlem2  15834  2lgsoddprmlem3a  15835  2lgsoddprmlem3b  15836  2lgsoddprmlem3c  15837  2lgsoddprmlem3d  15838  ex-exp  16323