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Theorem relfldext 31099
 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 31095 . 2 /FldExt = {⟨𝑒, 𝑓⟩ ∣ ((𝑒 ∈ Field ∧ 𝑓 ∈ Field) ∧ (𝑓 = (𝑒s (Base‘𝑓)) ∧ (Base‘𝑓) ∈ (SubRing‘𝑒)))}
21relopabiv 5681 1 Rel /FldExt
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 399   = wceq 1538   ∈ wcel 2115  Rel wrel 5548  ‘cfv 6344  (class class class)co 7150  Basecbs 16486   ↾s cress 16487  Fieldcfield 19506  SubRingcsubrg 19534  /FldExtcfldext 31091 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-v 3483  df-in 3927  df-ss 3937  df-opab 5116  df-xp 5549  df-rel 5550  df-fldext 31095 This theorem is referenced by:  extdgval  31107
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