Theorem cnre 11207

Description: Alias for ax-cnre 11179, 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 11179	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1541   ∈ wcel 2106  ∃wrex 3070  (class class class)co 7405  ℂcc 11104  ℝcr 11105  ici 11108   + caddc 11109   · cmul 11111

This theorem was proved from axioms:  ax-cnre 11179

This theorem is referenced by:  mulrid  11208  1re  11210  0re  11212  mul02  11388  cnegex  11391  0cnALT  11444  recex  11842  creur  12202  creui  12203  cju  12204  cnref1o  12965  replim  15059  ipasslem11  30080  sn-addlid  41273  sn-it0e0  41284  sn-negex12  41285  sn-mullid  41304  sn-0tie0  41308  sn-mul02  41309