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Theorem relfldext 32392
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 32388 . 2 /FldExt = {βŸ¨π‘’, π‘“βŸ© ∣ ((𝑒 ∈ Field ∧ 𝑓 ∈ Field) ∧ (𝑓 = (𝑒 β†Ύs (Baseβ€˜π‘“)) ∧ (Baseβ€˜π‘“) ∈ (SubRingβ€˜π‘’)))}
21relopabiv 5777 1 Rel /FldExt
Colors of variables: wff setvar class
Syntax hints:   ∧ wa 397   = wceq 1542   ∈ wcel 2107  Rel wrel 5639  β€˜cfv 6497  (class class class)co 7358  Basecbs 17088   β†Ύs cress 17117  Fieldcfield 20198  SubRingcsubrg 20232  /FldExtcfldext 32384
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-in 3918  df-ss 3928  df-opab 5169  df-xp 5640  df-rel 5641  df-fldext 32388
This theorem is referenced by:  extdgval  32400
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