Theorem cnre 10903

Description: Alias for ax-cnre 10875, 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 10875	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1539   ∈ wcel 2108  ∃wrex 3064  (class class class)co 7255  ℂcc 10800  ℝcr 10801  ici 10804   + caddc 10805   · cmul 10807

This theorem was proved from axioms:  ax-cnre 10875

This theorem is referenced by:  mulid1  10904  1re  10906  0re  10908  mul02  11083  cnegex  11086  0cnALT  11139  recex  11537  creur  11897  creui  11898  cju  11899  cnref1o  12654  replim  14755  ipasslem11  29103  sn-addid2  40308  sn-it0e0  40318  sn-negex12  40319  sn-mulid2  40338  sn-0tie0  40342  sn-mul02  40343