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Theorem relfldext 33674
Description: The field extension is a relation. (Contributed by Thierry Arnoux, 29-Jul-2023.)
Assertion
Ref Expression
relfldext Rel /FldExt

Proof of Theorem relfldext
Dummy variables 𝑒 𝑓 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-fldext 33670 . 2 /FldExt = {⟨𝑒, 𝑓⟩ ∣ ((𝑒 ∈ Field ∧ 𝑓 ∈ Field) ∧ (𝑓 = (𝑒s (Base‘𝑓)) ∧ (Base‘𝑓) ∈ (SubRing‘𝑒)))}
21relopabiv 5833 1 Rel /FldExt
Colors of variables: wff setvar class
Syntax hints:  wa 395   = wceq 1537  wcel 2106  Rel wrel 5694  cfv 6563  (class class class)co 7431  Basecbs 17245  s cress 17274  SubRingcsubrg 20586  Fieldcfield 20747  /FldExtcfldext 33666
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-opab 5211  df-xp 5695  df-rel 5696  df-fldext 33670
This theorem is referenced by:  extdgval  33682
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