Theorem cnre 10795

Description: Alias for ax-cnre 10767, 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 10767	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1543   ∈ wcel 2112  ∃wrex 3052  (class class class)co 7191  ℂcc 10692  ℝcr 10693  ici 10696   + caddc 10697   · cmul 10699

This theorem was proved from axioms:  ax-cnre 10767

This theorem is referenced by:  mulid1  10796  1re  10798  0re  10800  mul02  10975  cnegex  10978  0cnALT  11031  recex  11429  creur  11789  creui  11790  cju  11791  cnref1o  12546  replim  14644  ipasslem11  28875  sn-addid2  40036  sn-it0e0  40046  sn-negex12  40047  sn-mulid2  40066  sn-0tie0  40070  sn-mul02  40071