Theorem 7cn 9269

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 9268	. 2 ⊢ 7 ∈ ℝ
2	1	recni 8234	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 2202  ℂcc 8073  7c7 9241

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 2213  ax-resscn 8167  ax-1re 8169  ax-addrcl 8172

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3207  df-ss 3214  df-2 9244  df-3 9245  df-4 9246  df-5 9247  df-6 9248  df-7 9249

This theorem is referenced by:  8m1e7  9310  7p2e9  9337  7p3e10  9729  7t2e14  9763  7t4e28  9765  7t7e49  9768  cos2bnd  12384  2lgslem3d  15898