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Theorem relfldext 33697
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 33693 . 2 /FldExt = {⟨𝑒, 𝑓⟩ ∣ ((𝑒 ∈ Field ∧ 𝑓 ∈ Field) ∧ (𝑓 = (𝑒s (Base‘𝑓)) ∧ (Base‘𝑓) ∈ (SubRing‘𝑒)))}
21relopabiv 5830 1 Rel /FldExt
Colors of variables: wff setvar class
Syntax hints:  wa 395   = wceq 1540  wcel 2108  Rel wrel 5690  cfv 6561  (class class class)co 7431  Basecbs 17247  s cress 17274  SubRingcsubrg 20569  Fieldcfield 20730  /FldExtcfldext 33689
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-ss 3968  df-opab 5206  df-xp 5691  df-rel 5692  df-fldext 33693
This theorem is referenced by:  extdgval  33705
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