Theorem 3cn 7990

Description: The number 3 is a complex number. (Contributed by FL, 17-Oct-2010.)

Assertion

Ref	Expression
3cn	⊢ 3 ∈ ℂ

Proof of Theorem 3cn

Step	Hyp	Ref	Expression
1		3re 7989	. 2 ⊢ 3 ∈ ℝ
2	1	recni 7039	1 ⊢ 3 ∈ ℂ

Syntax hints:   ∈ wcel 1393  ℂcc 6887  3c3 7965

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-resscn 6976  ax-1re 6978  ax-addrcl 6981

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931  df-2 7973  df-3 7974

This theorem is referenced by:  3ex  7991  3m1e2  8036  3p2e5  8052  3p3e6  8053  4p4e8  8056  5p4e9  8059  6p4e10  8063  3t1e3  8070  3t2e6  8071  3t3e9  8072  8th4div3  8144  halfpm6th  8145  9t8e72  8468  fzo0to42pr  9076  sq3  9350  expnass  9357