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Mathbox for Thierry Arnoux |
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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 33311 | . 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 2105 Fieldcfield 20746 oRingcorng 33304 oFieldcofld 33305 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1539 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-v 3479 df-in 3969 df-ofld 33307 |
This theorem is referenced by: ofldlt1 33322 ofldchr 33323 |
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