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Mirrors > Home > MPE Home > Th. List > cnre | Structured version Visualization version GIF version |
Description: Alias for ax-cnre 10604, for naming consistency. (Contributed by NM, 3-Jan-2013.) |
Ref | Expression |
---|---|
cnre | ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-cnre 10604 | 1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1533 ∈ wcel 2110 ∃wrex 3139 (class class class)co 7150 ℂcc 10529 ℝcr 10530 ici 10533 + caddc 10534 · cmul 10536 |
This theorem was proved from axioms: ax-cnre 10604 |
This theorem is referenced by: mulid1 10633 1re 10635 0re 10637 mul02 10812 cnegex 10815 0cnALT 10868 recex 11266 creur 11626 creui 11627 cju 11628 cnref1o 12378 replim 14469 ipasslem11 28611 sn-addid2 39227 |
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