Theorem 8cn 9192

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 9191	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8154	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2200  ℂcc 7993  8c8 9163

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-resscn 8087  ax-1re 8089  ax-addrcl 8092

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3203  df-ss 3210  df-2 9165  df-3 9166  df-4 9167  df-5 9168  df-6 9169  df-7 9170  df-8 9171

This theorem is referenced by:  9m1e8  9232  8p2e10  9653  8t2e16  9688  8t5e40  9691  cos2bnd  12266  2exp11  12954  2exp16  12955  lgsdir2lem1  15701  lgsdir2lem5  15705  2lgslem3a  15766  2lgslem3b  15767  2lgslem3c  15768  2lgslem3d  15769  2lgslem3a1  15770  2lgslem3b1  15771  2lgslem3c1  15772  2lgslem3d1  15773  2lgsoddprmlem1  15778  2lgsoddprmlem2  15779  2lgsoddprmlem3a  15780  2lgsoddprmlem3b  15781  2lgsoddprmlem3c  15782  2lgsoddprmlem3d  15783  ex-exp  16049