Theorem 2cnALT 12233

Description: Alternate proof of 2cn 12232. Shorter but uses more axioms. Similar proofs are possible for 3cn 12238, ... , 9cn 12257. (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 12231	. 2 ⊢ 2 ∈ ℝ
2	1	recni 11158	1 ⊢ 2 ∈ ℂ

Syntax hints:   ∈ wcel 2114  ℂcc 11036  2c2 12212

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-resscn 11095  ax-1cn 11096  ax-icn 11097  ax-addcl 11098  ax-addrcl 11099  ax-mulcl 11100  ax-mulrcl 11101  ax-i2m1 11106  ax-1ne0 11107  ax-rrecex 11110  ax-cnre 11111

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ne 2934  df-ral 3053  df-rex 3063  df-rab 3402  df-v 3444  df-dif 3906  df-un 3908  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-uni 4866  df-br 5101  df-iota 6456  df-fv 6508  df-ov 7371  df-2 12220

This theorem is referenced by: (None)