Theorem 8cn 9070

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 9069	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8033	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2164  ℂcc 7872  8c8 9041

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175  ax-resscn 7966  ax-1re 7968  ax-addrcl 7971

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-in 3160  df-ss 3167  df-2 9043  df-3 9044  df-4 9045  df-5 9046  df-6 9047  df-7 9048  df-8 9049

This theorem is referenced by:  9m1e8  9110  8p2e10  9530  8t2e16  9565  8t5e40  9568  cos2bnd  11906  lgsdir2lem1  15185  lgsdir2lem5  15189  2lgslem3a  15250  2lgslem3b  15251  2lgslem3c  15252  2lgslem3d  15253  2lgslem3a1  15254  2lgslem3b1  15255  2lgslem3c1  15256  2lgslem3d1  15257  2lgsoddprmlem1  15262  2lgsoddprmlem2  15263  2lgsoddprmlem3a  15264  2lgsoddprmlem3b  15265  2lgsoddprmlem3c  15266  2lgsoddprmlem3d  15267  ex-exp  15289