Theorem cnre 11133

Description: Alias for ax-cnre 11103, 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 11103	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1542   ∈ wcel 2114  ∃wrex 3061  (class class class)co 7360  ℂcc 11028  ℝcr 11029  ici 11032   + caddc 11033   · cmul 11035

This theorem was proved from axioms:  ax-cnre 11103

This theorem is referenced by:  mulrid  11134  1re  11136  0re  11138  mul02  11315  cnegex  11318  0cnALT  11372  recex  11773  creur  12143  creui  12144  cju  12145  cnref1o  12902  replim  15043  ipasslem11  30898  sn-addlid  42695  sn-it0e0  42707  sn-negex12  42708  sn-mullid  42727  sn-0tie0  42742  sn-mul02  42743