Theorem 8cn 9369

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 9368	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8328	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2209  ℂcc 8167  8c8 9340

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220  ax-resscn 8261  ax-1re 8263  ax-addrcl 8266

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233  df-2 9342  df-3 9343  df-4 9344  df-5 9345  df-6 9346  df-7 9347  df-8 9348

This theorem is referenced by:  9m1e8  9409  8p2e10  9835  8t2e16  9870  8t5e40  9873  cos2bnd  12505  2exp11  13193  2exp16  13194  lgsdir2lem1  16061  lgsdir2lem5  16065  2lgslem3a  16126  2lgslem3b  16127  2lgslem3c  16128  2lgslem3d  16129  2lgslem3a1  16130  2lgslem3b1  16131  2lgslem3c1  16132  2lgslem3d1  16133  2lgsoddprmlem1  16138  2lgsoddprmlem2  16139  2lgsoddprmlem3a  16140  2lgsoddprmlem3b  16141  2lgsoddprmlem3c  16142  2lgsoddprmlem3d  16143  ex-exp  16655