Theorem 5cn 9313

Description: The number 5 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
5cn	⊢ 5 ∈ ℂ

Proof of Theorem 5cn

Step	Hyp	Ref	Expression
1		5re 9312	. 2 ⊢ 5 ∈ ℝ
2	1	recni 8282	1 ⊢ 5 ∈ ℂ

Syntax hints:   ∈ wcel 2203  ℂcc 8121  5c5 9287

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214  ax-resscn 8215  ax-1re 8217  ax-addrcl 8220

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-in 3216  df-ss 3223  df-2 9292  df-3 9293  df-4 9294  df-5 9295

This theorem is referenced by:  6m1e5  9356  5p2e7  9380  5p3e8  9381  5p4e9  9382  5p5e10  9775  5t2e10  9804  5recm6rec  9848  ef01bndlem  12435  5ndvds3  12613  5ndvds6  12614  dec5dvds  13103  dec5nprm  13105  2exp11  13127  2exp16  13128  lgsdir2lem1  15888  2lgslem3c  15955  2lgsoddprmlem3d  15970  ex-fac  16483