MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  cnre Structured version   Visualization version   GIF version

Theorem cnre 10626
Description: Alias for ax-cnre 10598, 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 10598 1 (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1528  wcel 2105  wrex 3136  (class class class)co 7145  cc 10523  cr 10524  ici 10527   + caddc 10528   · cmul 10530
This theorem was proved from axioms:  ax-cnre 10598
This theorem is referenced by:  mulid1  10627  1re  10629  0re  10631  mul02  10806  cnegex  10809  0cnALT  10862  recex  11260  creur  11620  creui  11621  cju  11622  cnref1o  12372  replim  14463  ipasslem11  28544  sn-addid2  39112
  Copyright terms: Public domain W3C validator