Theorem 7cn 8941

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 8940	. 2 ⊢ 7 ∈ ℝ
2	1	recni 7911	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 2136  ℂcc 7751  7c7 8913

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-11 1494  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147  ax-resscn 7845  ax-1re 7847  ax-addrcl 7850

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-in 3122  df-ss 3129  df-2 8916  df-3 8917  df-4 8918  df-5 8919  df-6 8920  df-7 8921

This theorem is referenced by:  8m1e7  8982  7p2e9  9008  7p3e10  9396  7t2e14  9430  7t4e28  9432  7t7e49  9435  cos2bnd  11701