Theorem 7cn 9388

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 9387	. 2 |- 7 e. RR
2	1	recni 8338	1 |- 7 e. CC

This proof depends on syntax axioms:   e. wcel 2209   CCcc 8177   7c7 9360

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220  ax-resscn 8271  ax-1re 8273  ax-addrcl 8276

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233  df-2 9363  df-3 9364  df-4 9365  df-5 9366  df-6 9367  df-7 9368

This theorem is used by:  8m1e7  9429  7p2e9  9456  7p3e10  9851  7t2e14  9885  7t4e28  9887  7t7e49  9890  cos2bnd  12527  log2ublem3  16085  log2ublog2  16086  2lgslem3d  16215