Theorem 7cn 9119

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 9118	. 2 ⊢ 7 ∈ ℝ
2	1	recni 8083	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 2175  ℂcc 7922  7c7 9091

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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-11 1528  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186  ax-resscn 8016  ax-1re 8018  ax-addrcl 8021

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-in 3171  df-ss 3178  df-2 9094  df-3 9095  df-4 9096  df-5 9097  df-6 9098  df-7 9099

This theorem is referenced by:  8m1e7  9160  7p2e9  9187  7p3e10  9577  7t2e14  9611  7t4e28  9613  7t7e49  9616  cos2bnd  12013  2lgslem3d  15515