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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 32690 | . 2 ⊢ (𝐹 ∈ oField ↔ (𝐹 ∈ Field ∧ 𝐹 ∈ oRing)) | |
2 | 1 | simplbi 496 | 1 ⊢ (𝐹 ∈ oField → 𝐹 ∈ Field) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2104 Fieldcfield 20501 oRingcorng 32683 oFieldcofld 32684 |
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 1911 ax-6 1969 ax-7 2009 ax-8 2106 ax-9 2114 ax-ext 2701 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1542 df-ex 1780 df-sb 2066 df-clab 2708 df-cleq 2722 df-clel 2808 df-v 3474 df-in 3954 df-ofld 32686 |
This theorem is referenced by: ofldlt1 32701 ofldchr 32702 |
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