Theorem 7cn 9227

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 9226	. 2 ⊢ 7 ∈ ℝ
2	1	recni 8191	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 2202  ℂcc 8030  7c7 9199

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 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-resscn 8124  ax-1re 8126  ax-addrcl 8129

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3206  df-ss 3213  df-2 9202  df-3 9203  df-4 9204  df-5 9205  df-6 9206  df-7 9207

This theorem is referenced by:  8m1e7  9268  7p2e9  9295  7p3e10  9685  7t2e14  9719  7t4e28  9721  7t7e49  9724  cos2bnd  12339  2lgslem3d  15844