Theorem 5cn 9367

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 9366	. 2 ⊢ 5 ∈ ℝ
2	1	recni 8332	1 ⊢ 5 ∈ ℂ

Syntax hints:   ∈ wcel 2209  ℂcc 8171  5c5 9341

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220  ax-resscn 8265  ax-1re 8267  ax-addrcl 8270

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233  df-2 9346  df-3 9347  df-4 9348  df-5 9349

This theorem is referenced by:  6m1e5  9410  5p2e7  9434  5p3e8  9435  5p4e9  9436  5p5e10  9830  5t2e10  9859  5recm6rec  9903  ef01bndlem  12506  5ndvds3  12684  5ndvds6  12685  dec5dvds  13174  dec5nprm  13176  2exp11  13198  2exp16  13199  log2ublem3  16068  log2ublog2  16069  lgsdir2lem1  16130  2lgslem3c  16197  2lgsoddprmlem3d  16212  ex-fac  16725