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Theorem 2cnALT 12228
Description: Alternate proof of 2cn 12227. Shorter but uses more axioms. Similar proofs are possible for 3cn 12233, ... , 9cn 12252. (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 12226 . 2 2 ∈ ℝ
21recni 11168 1 2 ∈ ℂ
Colors of variables: wff setvar class
Syntax hints:  wcel 2106  cc 11048  2c2 12207
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-resscn 11107  ax-1cn 11108  ax-icn 11109  ax-addcl 11110  ax-addrcl 11111  ax-mulcl 11112  ax-mulrcl 11113  ax-i2m1 11118  ax-1ne0 11119  ax-rrecex 11122  ax-cnre 11123
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-ne 2944  df-ral 3065  df-rex 3074  df-rab 3408  df-v 3447  df-dif 3913  df-un 3915  df-in 3917  df-ss 3927  df-nul 4283  df-if 4487  df-sn 4587  df-pr 4589  df-op 4593  df-uni 4866  df-br 5106  df-iota 6448  df-fv 6504  df-ov 7359  df-2 12215
This theorem is referenced by: (None)
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