Theorem cnre 11112

Description: Alias for ax-cnre 11082, 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 11082	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1540   ∈ wcel 2109  ∃wrex 3053  (class class class)co 7349  ℂcc 11007  ℝcr 11008  ici 11011   + caddc 11012   · cmul 11014

This theorem was proved from axioms:  ax-cnre 11082

This theorem is referenced by:  mulrid  11113  1re  11115  0re  11117  mul02  11294  cnegex  11297  0cnALT  11351  recex  11752  creur  12122  creui  12123  cju  12124  cnref1o  12886  replim  15023  ipasslem11  30784  sn-addlid  42381  sn-it0e0  42393  sn-negex12  42394  sn-mullid  42413  sn-0tie0  42428  sn-mul02  42429