Theorem 8cn 8571

Description: The number 8 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
8cn	⊢ 8 ∈ ℂ

Proof of Theorem 8cn

Step	Hyp	Ref	Expression
1		8re 8570	. 2 ⊢ 8 ∈ ℝ
2	1	recni 7563	1 ⊢ 8 ∈ ℂ

Syntax hints:   ∈ wcel 1439  ℂcc 7411  8c8 8542

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-resscn 7500  ax-1re 7502  ax-addrcl 7505

This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-in 3008  df-ss 3015  df-2 8544  df-3 8545  df-4 8546  df-5 8547  df-6 8548  df-7 8549  df-8 8550

This theorem is referenced by:  8p2e10  9019  8t2e16  9054  8t5e40  9057  cos2bnd  11114  ex-exp  11958