Theorem relfldext 33885

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.

Step	Hyp	Ref	Expression
1		df-fldext 33882	. 2 ⊢ /FldExt = {⟨𝑒, 𝑓⟩ ∣ ((𝑒 ∈ Field ∧ 𝑓 ∈ Field) ∧ (𝑓 = (𝑒 ↾s (Base‘𝑓)) ∧ (Base‘𝑓) ∈ (SubRing‘𝑒)))}
2	1	relopabiv 5782	1 ⊢ Rel /FldExt

Syntax hints:   ∧ wa 398   = wceq 1550   ∈ wcel 2132  Rel wrel 5641  ‘cfv 6506  (class class class)co 7381  Basecbs 17217   ↾_s cress 17238  SubRingcsubrg 20587  Fieldcfield 20748  /_FldExtcfldext 33879

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1805  ax-4 1819  ax-5 1920  ax-6 1977  ax-7 2018  ax-8 2134  ax-9 2142  ax-ext 2724

This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1553  df-ex 1790  df-sb 2081  df-clab 2731  df-cleq 2744  df-clel 2827  df-v 3446  df-ss 3912  df-opab 5153  df-xp 5642  df-rel 5643  df-fldext 33882

This theorem is referenced by:  extdgval  33894