Theorem 8cn 9219

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 9218	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8181	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2200  ℂcc 8020  8c8 9190

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 8114  ax-1re 8116  ax-addrcl 8119

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 3204  df-ss 3211  df-2 9192  df-3 9193  df-4 9194  df-5 9195  df-6 9196  df-7 9197  df-8 9198

This theorem is referenced by:  9m1e8  9259  8p2e10  9680  8t2e16  9715  8t5e40  9718  cos2bnd  12311  2exp11  12999  2exp16  13000  lgsdir2lem1  15747  lgsdir2lem5  15751  2lgslem3a  15812  2lgslem3b  15813  2lgslem3c  15814  2lgslem3d  15815  2lgslem3a1  15816  2lgslem3b1  15817  2lgslem3c1  15818  2lgslem3d1  15819  2lgsoddprmlem1  15824  2lgsoddprmlem2  15825  2lgsoddprmlem3a  15826  2lgsoddprmlem3b  15827  2lgsoddprmlem3c  15828  2lgsoddprmlem3d  15829  ex-exp  16259