Theorem isofld 26401

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

Step	Hyp	Ref	Expression
1		df-ofld 26397	. 2 |- oField = (Field i^i oRing )
2	1	elin2 3636	1 |- ( F e. oField <-> ( F e. Field /\ F e. oRing ) )

Syntax hints:   <-> wb 184   /\ wa 369   e. wcel 1758  Fieldcfield 16936  oRingcorng 26394  oFieldcofld 26395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2599  df-v 3067  df-in 3430  df-ofld 26397

This theorem is referenced by:  ofldfld  26409  ofldtos  26410  ofldlt1  26412  ofldchr  26413  subofld  26415  isarchiofld  26416  reofld  26439  nn0omnd  26440