Theorem 2cnALT 12248

Description: Alternate proof of 2cn 12247. Shorter but uses more axioms. Similar proofs are possible for 3cn 12253, ... , 9cn 12272. (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 12246	. 2 ⊢ 2 ∈ ℝ
2	1	recni 11150	1 ⊢ 2 ∈ ℂ

Syntax hints:   ∈ wcel 2114  ℂcc 11027  2c2 12227

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 11086  ax-1cn 11087  ax-icn 11088  ax-addcl 11089  ax-addrcl 11090  ax-mulcl 11091  ax-mulrcl 11092  ax-i2m1 11097  ax-1ne0 11098  ax-rrecex 11101  ax-cnre 11102

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 3391  df-v 3432  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-uni 4852  df-br 5087  df-iota 6448  df-fv 6500  df-ov 7363  df-2 12235

This theorem is referenced by: (None)