Theorem 8cn 9095

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 9094	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8057	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2167  ℂcc 7896  8c8 9066

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178  ax-resscn 7990  ax-1re 7992  ax-addrcl 7995

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-in 3163  df-ss 3170  df-2 9068  df-3 9069  df-4 9070  df-5 9071  df-6 9072  df-7 9073  df-8 9074

This theorem is referenced by:  9m1e8  9135  8p2e10  9555  8t2e16  9590  8t5e40  9593  cos2bnd  11944  2exp11  12632  2exp16  12633  lgsdir2lem1  15377  lgsdir2lem5  15381  2lgslem3a  15442  2lgslem3b  15443  2lgslem3c  15444  2lgslem3d  15445  2lgslem3a1  15446  2lgslem3b1  15447  2lgslem3c1  15448  2lgslem3d1  15449  2lgsoddprmlem1  15454  2lgsoddprmlem2  15455  2lgsoddprmlem3a  15456  2lgsoddprmlem3b  15457  2lgsoddprmlem3c  15458  2lgsoddprmlem3d  15459  ex-exp  15481