Theorem 8cn 9271

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 9270	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8234	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2202  ℂcc 8073  8c8 9242

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213  ax-resscn 8167  ax-1re 8169  ax-addrcl 8172

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3207  df-ss 3214  df-2 9244  df-3 9245  df-4 9246  df-5 9247  df-6 9248  df-7 9249  df-8 9250

This theorem is referenced by:  9m1e8  9311  8p2e10  9734  8t2e16  9769  8t5e40  9772  cos2bnd  12384  2exp11  13072  2exp16  13073  lgsdir2lem1  15830  lgsdir2lem5  15834  2lgslem3a  15895  2lgslem3b  15896  2lgslem3c  15897  2lgslem3d  15898  2lgslem3a1  15899  2lgslem3b1  15900  2lgslem3c1  15901  2lgslem3d1  15902  2lgsoddprmlem1  15907  2lgsoddprmlem2  15908  2lgsoddprmlem3a  15909  2lgsoddprmlem3b  15910  2lgsoddprmlem3c  15911  2lgsoddprmlem3d  15912  ex-exp  16424