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

Theorem cnre 10290
Description: Alias for ax-cnre 10262, 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 10262 1 (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1652  wcel 2155  wrex 3056  (class class class)co 6842  cc 10187  cr 10188  ici 10191   + caddc 10192   · cmul 10194
This theorem was proved from axioms:  ax-cnre 10262
This theorem is referenced by:  mulid1  10291  1re  10293  0re  10295  mul02  10468  cnegex  10471  recex  10913  creur  11268  creui  11269  cju  11270  cnref1o  12023  replim  14141  ipasslem11  28151
  Copyright terms: Public domain W3C validator