Theorem cnre 11277

Description: Alias for ax-cnre 11245, 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 11245	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

This proof depends on syntax axioms:   → wi 4   = wceq 1570   ∈ wcel 2145  ∃wrex 3086  (class class class)co 7408  ℂcc 11170  ℝcr 11171  ici 11174   + caddc 11175   · cmul 11177

This proof depends on axioms:  ax-cnre 11245

This theorem is used by:  mulrid  11278  1re  11280  0re  11282  mul02  11460  cnegex  11463  0cnALT  11517  recex  11918  creur  12284  creui  12285  cju  12286  cnref1o  13083  replim  15251  ipasslem11  31376  sn-addlid  43383  sn-it0e0  43395  sn-negex12  43396  sn-mullid  43415  sn-0tie0  43443  sn-mul02  43444