Theorem 7cn 9122

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 9121	. 2 |- 7 e. RR
2	1	recni 8086	1 |- 7 e. CC

Syntax hints:   e. wcel 2176   CCcc 7925   7c7 9094

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187  ax-resscn 8019  ax-1re 8021  ax-addrcl 8024

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-in 3172  df-ss 3179  df-2 9097  df-3 9098  df-4 9099  df-5 9100  df-6 9101  df-7 9102

This theorem is referenced by:  8m1e7  9163  7p2e9  9190  7p3e10  9580  7t2e14  9614  7t4e28  9616  7t7e49  9619  cos2bnd  12104  2lgslem3d  15606