Theorem cnre 10290

Description: Alias for ax-cnre 10262, 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 10262	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1652   ∈ wcel 2155  ∃wrex 3056  (class class class)co 6842  ℂcc 10187  ℝcr 10188  ici 10191   + caddc 10192   · cmul 10194

This theorem was proved from axioms:  ax-cnre 10262

This theorem is referenced by:  mulid1  10291  1re  10293  0re  10295  mul02  10468  cnegex  10471  recex  10913  creur  11268  creui  11269  cju  11270  cnref1o  12023  replim  14141  ipasslem11  28151