Theorem 7cn 9321

Description: The number 7 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
7cn	⊢ 7 ∈ ℂ

Proof of Theorem 7cn

Step	Hyp	Ref	Expression
1		7re 9320	. 2 ⊢ 7 ∈ ℝ
2	1	recni 8286	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 2203  ℂcc 8125  7c7 9293

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 2214  ax-resscn 8219  ax-1re 8221  ax-addrcl 8224

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-in 3217  df-ss 3224  df-2 9296  df-3 9297  df-4 9298  df-5 9299  df-6 9300  df-7 9301

This theorem is referenced by:  8m1e7  9362  7p2e9  9389  7p3e10  9783  7t2e14  9817  7t4e28  9819  7t7e49  9822  cos2bnd  12446  2lgslem3d  15969