Theorem 8cn 9068

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 9067	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8031	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2164  ℂcc 7870  8c8 9039

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 7964  ax-1re 7966  ax-addrcl 7969

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 3159  df-ss 3166  df-2 9041  df-3 9042  df-4 9043  df-5 9044  df-6 9045  df-7 9046  df-8 9047

This theorem is referenced by:  9m1e8  9108  8p2e10  9527  8t2e16  9562  8t5e40  9565  cos2bnd  11903  lgsdir2lem1  15144  lgsdir2lem5  15148  2lgsoddprmlem1  15193  2lgsoddprmlem2  15194  2lgsoddprmlem3a  15195  2lgsoddprmlem3b  15196  2lgsoddprmlem3c  15197  2lgsoddprmlem3d  15198  ex-exp  15219