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Theorem relfldext 33243
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 33239 . 2 /FldExt = {βŸ¨π‘’, π‘“βŸ© ∣ ((𝑒 ∈ Field ∧ 𝑓 ∈ Field) ∧ (𝑓 = (𝑒 β†Ύs (Baseβ€˜π‘“)) ∧ (Baseβ€˜π‘“) ∈ (SubRingβ€˜π‘’)))}
21relopabiv 5813 1 Rel /FldExt
Colors of variables: wff setvar class
Syntax hints:   ∧ wa 395   = wceq 1533   ∈ wcel 2098  Rel wrel 5674  β€˜cfv 6537  (class class class)co 7405  Basecbs 17153   β†Ύs cress 17182  SubRingcsubrg 20469  Fieldcfield 20588  /FldExtcfldext 33235
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-v 3470  df-in 3950  df-ss 3960  df-opab 5204  df-xp 5675  df-rel 5676  df-fldext 33239
This theorem is referenced by:  extdgval  33251
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