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Theorem ofldfld 33319
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 33311 . 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 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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