Theorem 2cnALT 12049

Description: Alternate proof of 2cn 12048. Shorter but uses more axioms. Similar proofs are possible for 3cn 12054, ... , 9cn 12073. (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 12047	. 2 ⊢ 2 ∈ ℝ
2	1	recni 10989	1 ⊢ 2 ∈ ℂ

Syntax hints:   ∈ wcel 2106  ℂcc 10869  2c2 12028

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709  ax-resscn 10928  ax-1cn 10929  ax-icn 10930  ax-addcl 10931  ax-addrcl 10932  ax-mulcl 10933  ax-mulrcl 10934  ax-i2m1 10939  ax-1ne0 10940  ax-rrecex 10943  ax-cnre 10944

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-ne 2944  df-ral 3069  df-rex 3070  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-uni 4840  df-br 5075  df-iota 6391  df-fv 6441  df-ov 7278  df-2 12036

This theorem is referenced by: (None)