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Theorem ofldfld 29784
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 29776 . 2 (𝐹 ∈ oField ↔ (𝐹 ∈ Field ∧ 𝐹 ∈ oRing))
21simplbi 476 1 (𝐹 ∈ oField → 𝐹 ∈ Field)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1988  Fieldcfield 18729  oRingcorng 29769  oFieldcofld 29770
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-v 3197  df-in 3574  df-ofld 29772
This theorem is referenced by:  ofldlt1  29787  ofldchr  29788
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