Theorem cnre 11204

Description: Alias for ax-cnre 11172, 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 11172	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1568   ∈ wcel 2141  ∃wrex 3087  (class class class)co 7410  ℂcc 11097  ℝcr 11098  ici 11101   + caddc 11102   · cmul 11104

This theorem was proved from axioms:  ax-cnre 11172

This theorem is referenced by:  mulrid  11205  1re  11207  0re  11209  mul02  11387  cnegex  11390  0cnALT  11444  recex  11845  creur  12211  creui  12212  cju  12213  cnref1o  13008  replim  15167  ipasslem11  31158  sn-addlid  43133  sn-it0e0  43145  sn-negex12  43146  sn-mullid  43165  sn-0tie0  43193  sn-mul02  43194