Theorem cnre 11193

Description: Alias for ax-cnre 11161, 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 11161	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1563   ∈ wcel 2145  ∃wrex 3089  (class class class)co 7400  ℂcc 11086  ℝcr 11087  ici 11090   + caddc 11091   · cmul 11093

This theorem was proved from axioms:  ax-cnre 11161

This theorem is referenced by:  mulrid  11194  1re  11196  0re  11198  mul02  11376  cnegex  11379  0cnALT  11433  recex  11834  creur  12203  creui  12204  cju  12205  cnref1o  13000  replim  15157  ipasslem11  31101  sn-addlid  43025  sn-it0e0  43037  sn-negex12  43038  sn-mullid  43057  sn-0tie0  43085  sn-mul02  43086