Theorem 5cn 9158

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 9157	. 2 ⊢ 5 ∈ ℝ
2	1	recni 8126	1 ⊢ 5 ∈ ℂ

Syntax hints:   ∈ wcel 2180  ℂcc 7965  5c5 9132

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 1473  ax-7 1474  ax-gen 1475  ax-ie1 1519  ax-ie2 1520  ax-8 1530  ax-11 1532  ax-4 1536  ax-17 1552  ax-i9 1556  ax-ial 1560  ax-i5r 1561  ax-ext 2191  ax-resscn 8059  ax-1re 8061  ax-addrcl 8064

This theorem depends on definitions:  df-bi 117  df-nf 1487  df-sb 1789  df-clab 2196  df-cleq 2202  df-clel 2205  df-in 3183  df-ss 3190  df-2 9137  df-3 9138  df-4 9139  df-5 9140

This theorem is referenced by:  6m1e5  9201  5p2e7  9225  5p3e8  9226  5p4e9  9227  5p5e10  9616  5t2e10  9645  5recm6rec  9689  ef01bndlem  12233  5ndvds3  12411  5ndvds6  12412  dec5dvds  12901  dec5nprm  12903  2exp11  12925  2exp16  12926  lgsdir2lem1  15672  2lgslem3c  15739  2lgsoddprmlem3d  15754  ex-fac  16002