Theorem 7cn 8506

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 8505	. 2 ⊢ 7 ∈ ℝ
2	1	recni 7500	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 1438  ℂcc 7348  7c7 8478

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-resscn 7437  ax-1re 7439  ax-addrcl 7442

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3005  df-ss 3012  df-2 8481  df-3 8482  df-4 8483  df-5 8484  df-6 8485  df-7 8486

This theorem is referenced by:  7p2e9  8567  7p3e10  8951  7t2e14  8985  7t4e28  8987  7t7e49  8990  cos2bnd  11051