Theorem cnre 11258

Description: Alias for ax-cnre 11228, 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 11228	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1540   ∈ wcel 2108  ∃wrex 3070  (class class class)co 7431  ℂcc 11153  ℝcr 11154  ici 11157   + caddc 11158   · cmul 11160

This theorem was proved from axioms:  ax-cnre 11228

This theorem is referenced by:  mulrid  11259  1re  11261  0re  11263  mul02  11439  cnegex  11442  0cnALT  11496  recex  11895  creur  12260  creui  12261  cju  12262  cnref1o  13027  replim  15155  ipasslem11  30859  sn-addlid  42434  sn-it0e0  42445  sn-negex12  42446  sn-mullid  42465  sn-0tie0  42469  sn-mul02  42470