Theorem cnre 10972

Description: Alias for ax-cnre 10944, 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 10944	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1539   ∈ wcel 2106  ∃wrex 3065  (class class class)co 7275  ℂcc 10869  ℝcr 10870  ici 10873   + caddc 10874   · cmul 10876

This theorem was proved from axioms:  ax-cnre 10944

This theorem is referenced by:  mulid1  10973  1re  10975  0re  10977  mul02  11153  cnegex  11156  0cnALT  11209  recex  11607  creur  11967  creui  11968  cju  11969  cnref1o  12725  replim  14827  ipasslem11  29202  sn-addid2  40387  sn-it0e0  40397  sn-negex12  40398  sn-mulid2  40417  sn-0tie0  40421  sn-mul02  40422