Theorem cnre 10436

Description: Alias for ax-cnre 10408, 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 10408	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1507   ∈ wcel 2050  ∃wrex 3090  (class class class)co 6976  ℂcc 10333  ℝcr 10334  ici 10337   + caddc 10338   · cmul 10340

This theorem was proved from axioms:  ax-cnre 10408

This theorem is referenced by:  mulid1  10437  1re  10439  0re  10441  mul02  10618  cnegex  10621  0cnALT  10674  recex  11073  creur  11433  creui  11434  cju  11435  cnref1o  12199  replim  14336  ipasslem11  28394