Theorem cnre 10632

Description: Alias for ax-cnre 10604, 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 10604	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1533   ∈ wcel 2110  ∃wrex 3139  (class class class)co 7150  ℂcc 10529  ℝcr 10530  ici 10533   + caddc 10534   · cmul 10536

This theorem was proved from axioms:  ax-cnre 10604

This theorem is referenced by:  mulid1  10633  1re  10635  0re  10637  mul02  10812  cnegex  10815  0cnALT  10868  recex  11266  creur  11626  creui  11627  cju  11628  cnref1o  12378  replim  14469  ipasslem11  28611  sn-addid2  39227