Theorem 8cn 9005

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 9004	. 2 ⊢ 8 ∈ ℝ
2	1	recni 7969	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2148  ℂcc 7809  8c8 8976

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-resscn 7903  ax-1re 7905  ax-addrcl 7908

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3136  df-ss 3143  df-2 8978  df-3 8979  df-4 8980  df-5 8981  df-6 8982  df-7 8983  df-8 8984

This theorem is referenced by:  9m1e8  9045  8p2e10  9463  8t2e16  9498  8t5e40  9501  cos2bnd  11768  lgsdir2lem1  14432  lgsdir2lem5  14436  2lgsoddprmlem1  14456  2lgsoddprmlem2  14457  2lgsoddprmlem3a  14458  2lgsoddprmlem3b  14459  2lgsoddprmlem3c  14460  2lgsoddprmlem3d  14461  ex-exp  14482