Theorem 8cn 9207

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 9206	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8169	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2200  ℂcc 8008  8c8 9178

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 8102  ax-1re 8104  ax-addrcl 8107

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 9180  df-3 9181  df-4 9182  df-5 9183  df-6 9184  df-7 9185  df-8 9186

This theorem is referenced by:  9m1e8  9247  8p2e10  9668  8t2e16  9703  8t5e40  9706  cos2bnd  12286  2exp11  12974  2exp16  12975  lgsdir2lem1  15722  lgsdir2lem5  15726  2lgslem3a  15787  2lgslem3b  15788  2lgslem3c  15789  2lgslem3d  15790  2lgslem3a1  15791  2lgslem3b1  15792  2lgslem3c1  15793  2lgslem3d1  15794  2lgsoddprmlem1  15799  2lgsoddprmlem2  15800  2lgsoddprmlem3a  15801  2lgsoddprmlem3b  15802  2lgsoddprmlem3c  15803  2lgsoddprmlem3d  15804  ex-exp  16146