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

Theorem cnre 11261
Description: Alias for ax-cnre 11231, 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 11231 1 (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1534  wcel 2099  wrex 3060  (class class class)co 7424  cc 11156  cr 11157  ici 11160   + caddc 11161   · cmul 11163
This theorem was proved from axioms:  ax-cnre 11231
This theorem is referenced by:  mulrid  11262  1re  11264  0re  11266  mul02  11442  cnegex  11445  0cnALT  11498  recex  11896  creur  12258  creui  12259  cju  12260  cnref1o  13021  replim  15121  ipasslem11  30773  sn-addlid  42184  sn-it0e0  42195  sn-negex12  42196  sn-mullid  42215  sn-0tie0  42219  sn-mul02  42220
  Copyright terms: Public domain W3C validator