Theorem 7cn 9155

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 9154	. 2 |- 7 e. RR
2	1	recni 8119	1 |- 7 e. CC

Syntax hints:   e. wcel 2178   CCcc 7958   7c7 9127

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 2189  ax-resscn 8052  ax-1re 8054  ax-addrcl 8057

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-in 3180  df-ss 3187  df-2 9130  df-3 9131  df-4 9132  df-5 9133  df-6 9134  df-7 9135

This theorem is referenced by:  8m1e7  9196  7p2e9  9223  7p3e10  9613  7t2e14  9647  7t4e28  9649  7t7e49  9652  cos2bnd  12186  2lgslem3d  15688