Theorem 8cn 9142

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 9141	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8104	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2177  ℂcc 7943  8c8 9113

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188  ax-resscn 8037  ax-1re 8039  ax-addrcl 8042

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-in 3176  df-ss 3183  df-2 9115  df-3 9116  df-4 9117  df-5 9118  df-6 9119  df-7 9120  df-8 9121

This theorem is referenced by:  9m1e8  9182  8p2e10  9603  8t2e16  9638  8t5e40  9641  cos2bnd  12146  2exp11  12834  2exp16  12835  lgsdir2lem1  15580  lgsdir2lem5  15584  2lgslem3a  15645  2lgslem3b  15646  2lgslem3c  15647  2lgslem3d  15648  2lgslem3a1  15649  2lgslem3b1  15650  2lgslem3c1  15651  2lgslem3d1  15652  2lgsoddprmlem1  15657  2lgsoddprmlem2  15658  2lgsoddprmlem3a  15659  2lgsoddprmlem3b  15660  2lgsoddprmlem3c  15661  2lgsoddprmlem3d  15662  ex-exp  15802