Theorem 8cn 9152

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 9151	. 2 ⊢ 8 ∈ ℝ
2	1	recni 8114	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 2177  ℂcc 7953  8c8 9123

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188  ax-resscn 8047  ax-1re 8049  ax-addrcl 8052

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-in 3176  df-ss 3183  df-2 9125  df-3 9126  df-4 9127  df-5 9128  df-6 9129  df-7 9130  df-8 9131

This theorem is referenced by:  9m1e8  9192  8p2e10  9613  8t2e16  9648  8t5e40  9651  cos2bnd  12156  2exp11  12844  2exp16  12845  lgsdir2lem1  15590  lgsdir2lem5  15594  2lgslem3a  15655  2lgslem3b  15656  2lgslem3c  15657  2lgslem3d  15658  2lgslem3a1  15659  2lgslem3b1  15660  2lgslem3c1  15661  2lgslem3d1  15662  2lgsoddprmlem1  15667  2lgsoddprmlem2  15668  2lgsoddprmlem3a  15669  2lgsoddprmlem3b  15670  2lgsoddprmlem3c  15671  2lgsoddprmlem3d  15672  ex-exp  15833