Theorem 9cn 9346

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 9345	. 2 ⊢ 9 ∈ ℝ
2	1	recni 8303	1 ⊢ 9 ∈ ℂ

Syntax hints:   ∈ wcel 2205  ℂcc 8142  9c9 9316

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216  ax-resscn 8236  ax-1re 8238  ax-addrcl 8241

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-in 3220  df-ss 3227  df-2 9317  df-3 9318  df-4 9319  df-5 9320  df-6 9321  df-7 9322  df-8 9323  df-9 9324

This theorem is referenced by:  10m1e9  9826  9t2e18  9852  9t8e72  9858  9t9e81  9859  9t11e99  9860  0.999...  12237  cos2bnd  12476  3dvds  12580  3dvdsdec  12581  3dvds2dec  12582  2exp8  13163