Theorem cnre 11261

Description: Alias for ax-cnre 11231, 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 11231	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1534   ∈ wcel 2099  ∃wrex 3060  (class class class)co 7424  ℂcc 11156  ℝcr 11157  ici 11160   + caddc 11161   · cmul 11163

This theorem was proved from axioms:  ax-cnre 11231

This theorem is referenced by:  mulrid  11262  1re  11264  0re  11266  mul02  11442  cnegex  11445  0cnALT  11498  recex  11896  creur  12258  creui  12259  cju  12260  cnref1o  13021  replim  15121  ipasslem11  30773  sn-addlid  42184  sn-it0e0  42195  sn-negex12  42196  sn-mullid  42215  sn-0tie0  42219  sn-mul02  42220