Theorem 8cn 9076

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 9075	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8038	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2167  ℂcc 7877  8c8 9047

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 7971  ax-1re 7973  ax-addrcl 7976

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 9049  df-3 9050  df-4 9051  df-5 9052  df-6 9053  df-7 9054  df-8 9055

This theorem is referenced by:  9m1e8  9116  8p2e10  9536  8t2e16  9571  8t5e40  9574  cos2bnd  11925  2exp11  12605  2exp16  12606  lgsdir2lem1  15269  lgsdir2lem5  15273  2lgslem3a  15334  2lgslem3b  15335  2lgslem3c  15336  2lgslem3d  15337  2lgslem3a1  15338  2lgslem3b1  15339  2lgslem3c1  15340  2lgslem3d1  15341  2lgsoddprmlem1  15346  2lgsoddprmlem2  15347  2lgsoddprmlem3a  15348  2lgsoddprmlem3b  15349  2lgsoddprmlem3c  15350  2lgsoddprmlem3d  15351  ex-exp  15373