Theorem 7cn 9033

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 9032	. 2 ⊢ 7 ∈ ℝ
2	1	recni 7999	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 2160  ℂcc 7839  7c7 9005

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-resscn 7933  ax-1re 7935  ax-addrcl 7938

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-in 3150  df-ss 3157  df-2 9008  df-3 9009  df-4 9010  df-5 9011  df-6 9012  df-7 9013

This theorem is referenced by:  8m1e7  9074  7p2e9  9100  7p3e10  9488  7t2e14  9522  7t4e28  9524  7t7e49  9527  cos2bnd  11800