Theorem 9cn 9194

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 9193	. 2 ⊢ 9 ∈ ℝ
2	1	recni 8154	1 ⊢ 9 ∈ ℂ

Syntax hints:   ∈ wcel 2200  ℂcc 7993  9c9 9164

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-resscn 8087  ax-1re 8089  ax-addrcl 8092

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3203  df-ss 3210  df-2 9165  df-3 9166  df-4 9167  df-5 9168  df-6 9169  df-7 9170  df-8 9171  df-9 9172

This theorem is referenced by:  10m1e9  9669  9t2e18  9695  9t8e72  9701  9t9e81  9702  9t11e99  9703  0.999...  12027  cos2bnd  12266  3dvds  12370  3dvdsdec  12371  3dvds2dec  12372  2exp8  12953