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Theorem isofld 28030
Description: An ordered field is a field with a total ordering compatible with its operations. (Contributed by Thierry Arnoux, 23-Mar-2018.)
Assertion
Ref Expression
isofld  |-  ( F  e. oField 
<->  ( F  e. Field  /\  F  e. oRing ) )

Proof of Theorem isofld
StepHypRef Expression
1 df-ofld 28026 . 2  |- oField  =  (Field 
i^i oRing )
21elin2 3675 1  |-  ( F  e. oField 
<->  ( F  e. Field  /\  F  e. oRing ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 367    e. wcel 1823  Fieldcfield 17595  oRingcorng 28023  oFieldcofld 28024
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3108  df-in 3468  df-ofld 28026
This theorem is referenced by:  ofldfld  28038  ofldtos  28039  ofldlt1  28041  ofldchr  28042  subofld  28044  isarchiofld  28045  reofld  28068  nn0omnd  28069
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