Theorem 7cn 9140

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 9139	. 2 |- 7 e. RR
2	1	recni 8104	1 |- 7 e. CC

Syntax hints:   e. wcel 2177   CCcc 7943   7c7 9112

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188  ax-resscn 8037  ax-1re 8039  ax-addrcl 8042

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-in 3176  df-ss 3183  df-2 9115  df-3 9116  df-4 9117  df-5 9118  df-6 9119  df-7 9120

This theorem is referenced by:  8m1e7  9181  7p2e9  9208  7p3e10  9598  7t2e14  9632  7t4e28  9634  7t7e49  9637  cos2bnd  12146  2lgslem3d  15648