Theorem 5cn 8913

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 8912	. 2 ⊢ 5 ∈ ℝ
2	1	recni 7890	1 ⊢ 5 ∈ ℂ

Syntax hints:   ∈ wcel 2128  ℂcc 7730  5c5 8887

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-resscn 7824  ax-1re 7826  ax-addrcl 7829

This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-in 3108  df-ss 3115  df-2 8892  df-3 8893  df-4 8894  df-5 8895

This theorem is referenced by:  6m1e5  8956  5p2e7  8979  5p3e8  8980  5p4e9  8981  5p5e10  9365  5t2e10  9394  5recm6rec  9438  ef01bndlem  11653  ex-fac  13304