Theorem 9cn 9124

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 9123	. 2 ⊢ 9 ∈ ℝ
2	1	recni 8084	1 ⊢ 9 ∈ ℂ

Syntax hints:   ∈ wcel 2176  ℂcc 7923  9c9 9094

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187  ax-resscn 8017  ax-1re 8019  ax-addrcl 8022

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-in 3172  df-ss 3179  df-2 9095  df-3 9096  df-4 9097  df-5 9098  df-6 9099  df-7 9100  df-8 9101  df-9 9102

This theorem is referenced by:  10m1e9  9599  9t2e18  9625  9t8e72  9631  9t9e81  9632  9t11e99  9633  0.999...  11832  cos2bnd  12071  3dvds  12175  3dvdsdec  12176  3dvds2dec  12177  2exp8  12758