Theorem 8cn 9122

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 9121	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8084	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2176  ℂcc 7923  8c8 9093

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187  ax-resscn 8017  ax-1re 8019  ax-addrcl 8022

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-in 3172  df-ss 3179  df-2 9095  df-3 9096  df-4 9097  df-5 9098  df-6 9099  df-7 9100  df-8 9101

This theorem is referenced by:  9m1e8  9162  8p2e10  9583  8t2e16  9618  8t5e40  9621  cos2bnd  12071  2exp11  12759  2exp16  12760  lgsdir2lem1  15505  lgsdir2lem5  15509  2lgslem3a  15570  2lgslem3b  15571  2lgslem3c  15572  2lgslem3d  15573  2lgslem3a1  15574  2lgslem3b1  15575  2lgslem3c1  15576  2lgslem3d1  15577  2lgsoddprmlem1  15582  2lgsoddprmlem2  15583  2lgsoddprmlem3a  15584  2lgsoddprmlem3b  15585  2lgsoddprmlem3c  15586  2lgsoddprmlem3d  15587  ex-exp  15663