Theorem cnre 11130

Description: Alias for ax-cnre 11100, 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 11100	1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦)))

Syntax hints:   → wi 4   = wceq 1542   ∈ wcel 2114  ∃wrex 3062  (class class class)co 7358  ℂcc 11025  ℝcr 11026  ici 11029   + caddc 11030   · cmul 11032

This theorem was proved from axioms:  ax-cnre 11100

This theorem is referenced by:  mulrid  11131  1re  11133  0re  11135  mul02  11313  cnegex  11316  0cnALT  11370  recex  11771  creur  12142  creui  12143  cju  12144  cnref1o  12924  replim  15067  ipasslem11  30931  sn-addlid  42847  sn-it0e0  42859  sn-negex12  42860  sn-mullid  42879  sn-0tie0  42907  sn-mul02  42908