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Theorem cnre 10627
 Description: Alias for ax-cnre 10599, 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 10599 1 (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538   ∈ wcel 2111  ∃wrex 3107  (class class class)co 7135  ℂcc 10524  ℝcr 10525  ici 10528   + caddc 10529   · cmul 10531 This theorem was proved from axioms:  ax-cnre 10599 This theorem is referenced by:  mulid1  10628  1re  10630  0re  10632  mul02  10807  cnegex  10810  0cnALT  10863  recex  11261  creur  11619  creui  11620  cju  11621  cnref1o  12372  replim  14467  ipasslem11  28623  sn-addid2  39540  sn-it0e0  39550  sn-negex12  39551  sn-mulid2  39570  sn-0tie0  39574  sn-mul02  39575
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