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Theorem ofldfld 33340
Description: An ordered field is a field. (Contributed by Thierry Arnoux, 20-Jan-2018.)
Assertion
Ref Expression
ofldfld (𝐹 ∈ oField → 𝐹 ∈ Field)

Proof of Theorem ofldfld
StepHypRef Expression
1 isofld 33332 . 2 (𝐹 ∈ oField ↔ (𝐹 ∈ Field ∧ 𝐹 ∈ oRing))
21simplbi 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
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