Theorem 7cn 9003

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 9002	. 2 ⊢ 7 ∈ ℝ
2	1	recni 7969	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 2148  ℂcc 7809  7c7 8975

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-resscn 7903  ax-1re 7905  ax-addrcl 7908

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3136  df-ss 3143  df-2 8978  df-3 8979  df-4 8980  df-5 8981  df-6 8982  df-7 8983

This theorem is referenced by:  8m1e7  9044  7p2e9  9070  7p3e10  9458  7t2e14  9492  7t4e28  9494  7t7e49  9497  cos2bnd  11768