Theorem cnre 11287

Description: Alias for ax-cnre 11257, 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 11257	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1537   ∈ wcel 2108  ∃wrex 3076  (class class class)co 7448  ℂcc 11182  ℝcr 11183  ici 11186   + caddc 11187   · cmul 11189

This theorem was proved from axioms:  ax-cnre 11257

This theorem is referenced by:  mulrid  11288  1re  11290  0re  11292  mul02  11468  cnegex  11471  0cnALT  11524  recex  11922  creur  12287  creui  12288  cju  12289  cnref1o  13050  replim  15165  ipasslem11  30872  sn-addlid  42380  sn-it0e0  42391  sn-negex12  42392  sn-mullid  42411  sn-0tie0  42415  sn-mul02  42416