Theorem cnre 11042

Description: Alias for ax-cnre 11014, 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 11014	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1540   ∈ wcel 2105  ∃wrex 3071  (class class class)co 7313  ℂcc 10939  ℝcr 10940  ici 10943   + caddc 10944   · cmul 10946

This theorem was proved from axioms:  ax-cnre 11014

This theorem is referenced by:  mulid1  11043  1re  11045  0re  11047  mul02  11223  cnegex  11226  0cnALT  11279  recex  11677  creur  12037  creui  12038  cju  12039  cnref1o  12795  replim  14896  ipasslem11  29310  sn-addid2  40597  sn-it0e0  40607  sn-negex12  40608  sn-mulid2  40627  sn-0tie0  40631  sn-mul02  40632