Theorem cnre 11178

Description: Alias for ax-cnre 11148, 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 11148	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1540   ∈ wcel 2109  ∃wrex 3054  (class class class)co 7390  ℂcc 11073  ℝcr 11074  ici 11077   + caddc 11078   · cmul 11080

This theorem was proved from axioms:  ax-cnre 11148

This theorem is referenced by:  mulrid  11179  1re  11181  0re  11183  mul02  11359  cnegex  11362  0cnALT  11416  recex  11817  creur  12187  creui  12188  cju  12189  cnref1o  12951  replim  15089  ipasslem11  30776  sn-addlid  42399  sn-it0e0  42411  sn-negex12  42412  sn-mullid  42431  sn-0tie0  42446  sn-mul02  42447