Theorem 7cn 8917

Description: The number 7 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
7cn	|- 7 e. CC

Proof of Theorem 7cn

Step	Hyp	Ref	Expression
1		7re 8916	. 2 |- 7 e. RR
2	1	recni 7890	1 |- 7 e. CC

Syntax hints:   e. wcel 2128   CCcc 7730   7c7 8889

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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-resscn 7824  ax-1re 7826  ax-addrcl 7829

This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-in 3108  df-ss 3115  df-2 8892  df-3 8893  df-4 8894  df-5 8895  df-6 8896  df-7 8897

This theorem is referenced by:  8m1e7  8958  7p2e9  8984  7p3e10  9369  7t2e14  9403  7t4e28  9405  7t7e49  9408  cos2bnd  11657