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Mirrors > Home > MPE Home > Th. List > cnre | Structured version Visualization version GIF version |
Description: Alias for ax-cnre 10598, 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 10598 | 1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1528 ∈ wcel 2105 ∃wrex 3136 (class class class)co 7145 ℂcc 10523 ℝcr 10524 ici 10527 + caddc 10528 · cmul 10530 |
This theorem was proved from axioms: ax-cnre 10598 |
This theorem is referenced by: mulid1 10627 1re 10629 0re 10631 mul02 10806 cnegex 10809 0cnALT 10862 recex 11260 creur 11620 creui 11621 cju 11622 cnref1o 12372 replim 14463 ipasslem11 28544 sn-addid2 39112 |
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