Theorem 5cn 9001

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 9000	. 2 ⊢ 5 ∈ ℝ
2	1	recni 7971	1 ⊢ 5 ∈ ℂ

Syntax hints:   ∈ wcel 2148  ℂcc 7811  5c5 8975

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-resscn 7905  ax-1re 7907  ax-addrcl 7910

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3137  df-ss 3144  df-2 8980  df-3 8981  df-4 8982  df-5 8983

This theorem is referenced by:  6m1e5  9044  5p2e7  9067  5p3e8  9068  5p4e9  9069  5p5e10  9456  5t2e10  9485  5recm6rec  9529  ef01bndlem  11766  lgsdir2lem1  14514  2lgsoddprmlem3d  14543  ex-fac  14565