| Mathbox for Thierry Arnoux |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > Mathboxes > ofldfld | Structured version Visualization version GIF version | ||
| Description: An ordered field is a field. (Contributed by Thierry Arnoux, 20-Jan-2018.) |
| Ref | Expression |
|---|---|
| ofldfld | ⊢ (𝐹 ∈ oField → 𝐹 ∈ Field) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | isofld 33332 | . 2 ⊢ (𝐹 ∈ oField ↔ (𝐹 ∈ Field ∧ 𝐹 ∈ oRing)) | |
| 2 | 1 | simplbi 497 | 1 ⊢ (𝐹 ∈ oField → 𝐹 ∈ Field) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∈ wcel 2108 Fieldcfield 20730 oRingcorng 33325 oFieldcofld 33326 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-in 3958 df-ofld 33328 |
| This theorem is referenced by: ofldlt1 33343 ofldchr 33344 |
| Copyright terms: Public domain | W3C validator |