Theorem cnre 11147

Description: Alias for ax-cnre 11117, 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 11117	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1540   ∈ wcel 2109  ∃wrex 3053  (class class class)co 7369  ℂcc 11042  ℝcr 11043  ici 11046   + caddc 11047   · cmul 11049

This theorem was proved from axioms:  ax-cnre 11117

This theorem is referenced by:  mulrid  11148  1re  11150  0re  11152  mul02  11328  cnegex  11331  0cnALT  11385  recex  11786  creur  12156  creui  12157  cju  12158  cnref1o  12920  replim  15058  ipasslem11  30819  sn-addlid  42385  sn-it0e0  42397  sn-negex12  42398  sn-mullid  42417  sn-0tie0  42432  sn-mul02  42433