Theorem 2cnALT 12349

Description: Alternate proof of 2cn 12348. Shorter but uses more axioms. Similar proofs are possible for 3cn 12354, ... , 9cn 12373. (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 12347	. 2 ⊢ 2 ∈ ℝ
2	1	recni 11282	1 ⊢ 2 ∈ ℂ

Syntax hints:   ∈ wcel 2108  ℂcc 11160  2c2 12328

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-resscn 11219  ax-1cn 11220  ax-icn 11221  ax-addcl 11222  ax-addrcl 11223  ax-mulcl 11224  ax-mulrcl 11225  ax-i2m1 11230  ax-1ne0 11231  ax-rrecex 11234  ax-cnre 11235

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3483  df-dif 3969  df-un 3971  df-ss 3983  df-nul 4343  df-if 4535  df-sn 4635  df-pr 4637  df-op 4641  df-uni 4916  df-br 5152  df-iota 6522  df-fv 6577  df-ov 7441  df-2 12336

This theorem is referenced by: (None)