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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 31091 | . 2 ⊢ (𝐹 ∈ oField ↔ (𝐹 ∈ Field ∧ 𝐹 ∈ oRing)) | |
2 | 1 | simplbi 501 | 1 ⊢ (𝐹 ∈ oField → 𝐹 ∈ Field) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2114 Fieldcfield 19635 oRingcorng 31084 oFieldcofld 31085 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-ext 2711 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1545 df-ex 1787 df-sb 2075 df-clab 2718 df-cleq 2731 df-clel 2812 df-v 3402 df-in 3860 df-ofld 31087 |
This theorem is referenced by: ofldlt1 31102 ofldchr 31103 |
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