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Theorem ofldfld 31509
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 31501 . 2 (𝐹 ∈ oField ↔ (𝐹 ∈ Field ∧ 𝐹 ∈ oRing))
21simplbi 498 1 (𝐹 ∈ oField → 𝐹 ∈ Field)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Fieldcfield 19992  oRingcorng 31494  oFieldcofld 31495
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ofld 31497
This theorem is referenced by:  ofldlt1  31512  ofldchr  31513
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