Theorem 8cn 9121

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 9120	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8083	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2175  ℂcc 7922  8c8 9092

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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-11 1528  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186  ax-resscn 8016  ax-1re 8018  ax-addrcl 8021

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-in 3171  df-ss 3178  df-2 9094  df-3 9095  df-4 9096  df-5 9097  df-6 9098  df-7 9099  df-8 9100

This theorem is referenced by:  9m1e8  9161  8p2e10  9582  8t2e16  9617  8t5e40  9620  cos2bnd  12042  2exp11  12730  2exp16  12731  lgsdir2lem1  15476  lgsdir2lem5  15480  2lgslem3a  15541  2lgslem3b  15542  2lgslem3c  15543  2lgslem3d  15544  2lgslem3a1  15545  2lgslem3b1  15546  2lgslem3c1  15547  2lgslem3d1  15548  2lgsoddprmlem1  15553  2lgsoddprmlem2  15554  2lgsoddprmlem3a  15555  2lgsoddprmlem3b  15556  2lgsoddprmlem3c  15557  2lgsoddprmlem3d  15558  ex-exp  15625