Theorem 5cn 9337

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 9336	. 2 ⊢ 5 ∈ ℝ
2	1	recni 8302	1 ⊢ 5 ∈ ℂ

Syntax hints:   ∈ wcel 2205  ℂcc 8141  5c5 9311

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 2216  ax-resscn 8235  ax-1re 8237  ax-addrcl 8240

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-in 3220  df-ss 3227  df-2 9316  df-3 9317  df-4 9318  df-5 9319

This theorem is referenced by:  6m1e5  9380  5p2e7  9404  5p3e8  9405  5p4e9  9406  5p5e10  9800  5t2e10  9829  5recm6rec  9873  ef01bndlem  12470  5ndvds3  12648  5ndvds6  12649  dec5dvds  13138  dec5nprm  13140  2exp11  13162  2exp16  13163  lgsdir2lem1  16030  2lgslem3c  16097  2lgsoddprmlem3d  16112  ex-fac  16625