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Theorem cnre 11256
Description: Alias for ax-cnre 11226, for naming consistency. (Contributed by NM, 3-Jan-2013.)
Assertion
Ref Expression
cnre (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))
Distinct variable group:   𝑥,𝐴,𝑦

Proof of Theorem cnre
StepHypRef Expression
1 ax-cnre 11226 1 (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537  wcel 2106  wrex 3068  (class class class)co 7431  cc 11151  cr 11152  ici 11155   + caddc 11156   · cmul 11158
This theorem was proved from axioms:  ax-cnre 11226
This theorem is referenced by:  mulrid  11257  1re  11259  0re  11261  mul02  11437  cnegex  11440  0cnALT  11494  recex  11893  creur  12258  creui  12259  cju  12260  cnref1o  13025  replim  15152  ipasslem11  30869  sn-addlid  42411  sn-it0e0  42422  sn-negex12  42423  sn-mullid  42442  sn-0tie0  42446  sn-mul02  42447
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