Theorem 7cn 9091

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 9090	. 2 |- 7 e. RR
2	1	recni 8055	1 |- 7 e. CC

Syntax hints:   e. wcel 2167   CCcc 7894   7c7 9063

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178  ax-resscn 7988  ax-1re 7990  ax-addrcl 7993

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-in 3163  df-ss 3170  df-2 9066  df-3 9067  df-4 9068  df-5 9069  df-6 9070  df-7 9071

This theorem is referenced by:  8m1e7  9132  7p2e9  9159  7p3e10  9548  7t2e14  9582  7t4e28  9584  7t7e49  9587  cos2bnd  11942  2lgslem3d  15421