Theorem 2cnALT 12208

Description: Alternate proof of 2cn 12207. Shorter but uses more axioms. Similar proofs are possible for 3cn 12213, ... , 9cn 12232. (Contributed by NM, 30-Jul-2004.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
2cnALT	⊢ 2 ∈ ℂ

Proof of Theorem 2cnALT

Step	Hyp	Ref	Expression
1		2re 12206	. 2 ⊢ 2 ∈ ℝ
2	1	recni 11133	1 ⊢ 2 ∈ ℂ

Syntax hints:   ∈ wcel 2113  ℂcc 11011  2c2 12187

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705  ax-resscn 11070  ax-1cn 11071  ax-icn 11072  ax-addcl 11073  ax-addrcl 11074  ax-mulcl 11075  ax-mulrcl 11076  ax-i2m1 11081  ax-1ne0 11082  ax-rrecex 11085  ax-cnre 11086

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-ne 2930  df-ral 3049  df-rex 3058  df-rab 3397  df-v 3439  df-dif 3901  df-un 3903  df-ss 3915  df-nul 4283  df-if 4475  df-sn 4576  df-pr 4578  df-op 4582  df-uni 4859  df-br 5094  df-iota 6442  df-fv 6494  df-ov 7355  df-2 12195

This theorem is referenced by: (None)