Theorem 9cn 9038

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 9037	. 2 ⊢ 9 ∈ ℝ
2	1	recni 8000	1 ⊢ 9 ∈ ℂ

Syntax hints:   ∈ wcel 2160  ℂcc 7840  9c9 9008

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-resscn 7934  ax-1re 7936  ax-addrcl 7939

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-in 3150  df-ss 3157  df-2 9009  df-3 9010  df-4 9011  df-5 9012  df-6 9013  df-7 9014  df-8 9015  df-9 9016

This theorem is referenced by:  10m1e9  9510  9t2e18  9536  9t8e72  9542  9t9e81  9543  9t11e99  9544  0.999...  11564  cos2bnd  11803  3dvdsdec  11905  3dvds2dec  11906