Theorem cnre 11141

Description: Alias for ax-cnre 11111, 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 11111	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1542   ∈ wcel 2114  ∃wrex 3062  (class class class)co 7367  ℂcc 11036  ℝcr 11037  ici 11040   + caddc 11041   · cmul 11043

This theorem was proved from axioms:  ax-cnre 11111

This theorem is referenced by:  mulrid  11142  1re  11144  0re  11146  mul02  11324  cnegex  11327  0cnALT  11381  recex  11782  creur  12153  creui  12154  cju  12155  cnref1o  12935  replim  15078  ipasslem11  30911  sn-addlid  42836  sn-it0e0  42848  sn-negex12  42849  sn-mullid  42868  sn-0tie0  42896  sn-mul02  42897