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Theorem 2cnALT 11509
 Description: Alternate proof of 2cn 11508. Shorter but uses more axioms. Similar proofs are possible for 3cn 11514, ... , 9cn 11539. (Contributed by NM, 30-Jul-2004.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
2cnALT 2 ∈ ℂ

Proof of Theorem 2cnALT
StepHypRef Expression
1 2re 11507 . 2 2 ∈ ℝ
21recni 10446 1 2 ∈ ℂ
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2048  ℂcc 10325  2c2 11488 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1964  ax-8 2050  ax-9 2057  ax-10 2077  ax-11 2091  ax-12 2104  ax-ext 2745  ax-resscn 10384  ax-1cn 10385  ax-icn 10386  ax-addcl 10387  ax-addrcl 10388  ax-mulcl 10389  ax-mulrcl 10390  ax-i2m1 10395  ax-1ne0 10396  ax-rrecex 10399  ax-cnre 10400 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2014  df-clab 2754  df-cleq 2765  df-clel 2840  df-nfc 2912  df-ne 2962  df-ral 3087  df-rex 3088  df-rab 3091  df-v 3411  df-dif 3828  df-un 3830  df-in 3832  df-ss 3839  df-nul 4174  df-if 4345  df-sn 4436  df-pr 4438  df-op 4442  df-uni 4707  df-br 4924  df-iota 6146  df-fv 6190  df-ov 6973  df-2 11496 This theorem is referenced by: (None)
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