Theorem 7cn 8828

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 8827	. 2 ⊢ 7 ∈ ℝ
2	1	recni 7802	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 1481  ℂcc 7642  7c7 8800

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-resscn 7736  ax-1re 7738  ax-addrcl 7741

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3082  df-ss 3089  df-2 8803  df-3 8804  df-4 8805  df-5 8806  df-6 8807  df-7 8808

This theorem is referenced by:  8m1e7  8869  7p2e9  8895  7p3e10  9280  7t2e14  9314  7t4e28  9316  7t7e49  9319  cos2bnd  11503