Theorem 7cn 9217

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 9216	. 2 ⊢ 7 ∈ ℝ
2	1	recni 8181	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 2200  ℂcc 8020  7c7 9189

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-resscn 8114  ax-1re 8116  ax-addrcl 8119

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3204  df-ss 3211  df-2 9192  df-3 9193  df-4 9194  df-5 9195  df-6 9196  df-7 9197

This theorem is referenced by:  8m1e7  9258  7p2e9  9285  7p3e10  9675  7t2e14  9709  7t4e28  9711  7t7e49  9714  cos2bnd  12311  2lgslem3d  15815