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Theorem 2cnALT 12263
Description: Alternate proof of 2cn 12262. Shorter but uses more axioms. Similar proofs are possible for 3cn 12268, ... , 9cn 12287. (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 12261 . 2 2 ∈ ℝ
21recni 11194 1 2 ∈ ℂ
Colors of variables: wff setvar class
Syntax hints:  wcel 2109  cc 11072  2c2 12242
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702  ax-resscn 11131  ax-1cn 11132  ax-icn 11133  ax-addcl 11134  ax-addrcl 11135  ax-mulcl 11136  ax-mulrcl 11137  ax-i2m1 11142  ax-1ne0 11143  ax-rrecex 11146  ax-cnre 11147
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-ne 2927  df-ral 3046  df-rex 3055  df-rab 3409  df-v 3452  df-dif 3919  df-un 3921  df-ss 3933  df-nul 4299  df-if 4491  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4874  df-br 5110  df-iota 6466  df-fv 6521  df-ov 7392  df-2 12250
This theorem is referenced by: (None)
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