Theorem cnre 11149

Description: Alias for ax-cnre 11119, 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 11119	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 11044  ℝcr 11045  ici 11048   + caddc 11049   · cmul 11051

This theorem was proved from axioms:  ax-cnre 11119

This theorem is referenced by:  mulrid  11150  1re  11152  0re  11154  mul02  11330  cnegex  11333  0cnALT  11387  recex  11788  creur  12158  creui  12159  cju  12160  cnref1o  12922  replim  15059  ipasslem11  30820  sn-addlid  42386  sn-it0e0  42398  sn-negex12  42399  sn-mullid  42418  sn-0tie0  42433  sn-mul02  42434