|   | Metamath Proof Explorer | < Previous  
      Next > Nearby theorems | |
| Mirrors > Home > MPE Home > Th. List > cnre | Structured version Visualization version GIF version | ||
| Description: Alias for ax-cnre 11228, 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 11228 | 1 ⊢ (𝐴 ∈ ℂ → ∃𝑥 ∈ ℝ ∃𝑦 ∈ ℝ 𝐴 = (𝑥 + (i · 𝑦))) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 = wceq 1540 ∈ wcel 2108 ∃wrex 3070 (class class class)co 7431 ℂcc 11153 ℝcr 11154 ici 11157 + caddc 11158 · cmul 11160 | 
| This theorem was proved from axioms: ax-cnre 11228 | 
| This theorem is referenced by: mulrid 11259 1re 11261 0re 11263 mul02 11439 cnegex 11442 0cnALT 11496 recex 11895 creur 12260 creui 12261 cju 12262 cnref1o 13027 replim 15155 ipasslem11 30859 sn-addlid 42434 sn-it0e0 42445 sn-negex12 42446 sn-mullid 42465 sn-0tie0 42469 sn-mul02 42470 | 
| Copyright terms: Public domain | W3C validator |