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

Step	Hyp	Ref	Expression
1		ax-cnre 11226	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1537   ∈ wcel 2106  ∃wrex 3068  (class class class)co 7431  ℂcc 11151  ℝcr 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