Theorem 9cn 9231

Description: The number 9 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
9cn	⊢ 9 ∈ ℂ

Proof of Theorem 9cn

Step	Hyp	Ref	Expression
1		9re 9230	. 2 ⊢ 9 ∈ ℝ
2	1	recni 8191	1 ⊢ 9 ∈ ℂ

Syntax hints:   ∈ wcel 2202  ℂcc 8030  9c9 9201

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 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-resscn 8124  ax-1re 8126  ax-addrcl 8129

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3206  df-ss 3213  df-2 9202  df-3 9203  df-4 9204  df-5 9205  df-6 9206  df-7 9207  df-8 9208  df-9 9209

This theorem is referenced by:  10m1e9  9706  9t2e18  9732  9t8e72  9738  9t9e81  9739  9t11e99  9740  0.999...  12100  cos2bnd  12339  3dvds  12443  3dvdsdec  12444  3dvds2dec  12445  2exp8  13026