Theorem cnre 10248

Description: Alias for ax-cnre 10221, 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 10221	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1632   ∈ wcel 2139  ∃wrex 3051  (class class class)co 6814  ℂcc 10146  ℝcr 10147  ici 10150   + caddc 10151   · cmul 10153

This theorem was proved from axioms:  ax-cnre 10221

This theorem is referenced by:  mulid1  10249  1re  10251  mul02  10426  cnegex  10429  recex  10871  creur  11226  creui  11227  cju  11228  cnref1o  12040  replim  14075  ipasslem11  28025