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Theorem relcoels 38406
Description: Coelements on 𝐴 is a relation. (Contributed by Peter Mazsa, 5-Oct-2021.)
Assertion
Ref Expression
relcoels Rel ∼ 𝐴

Proof of Theorem relcoels
StepHypRef Expression
1 relcoss 38405 . 2 Rel ≀ ( E ↾ 𝐴)
2 df-coels 38394 . . 3 𝐴 = ≀ ( E ↾ 𝐴)
32releqi 5790 . 2 (Rel ∼ 𝐴 ↔ Rel ≀ ( E ↾ 𝐴))
41, 3mpbir 231 1 Rel ∼ 𝐴
Colors of variables: wff setvar class
Syntax hints:   E cep 5588  ccnv 5688  cres 5691  Rel wrel 5694  ccoss 38162  ccoels 38163
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-opab 5211  df-xp 5695  df-rel 5696  df-coss 38393  df-coels 38394
This theorem is referenced by:  erimeq2  38660
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