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Theorem relcoels 36547
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 36546 . 2 Rel ≀ ( E ↾ 𝐴)
2 df-coels 36538 . . 3 𝐴 = ≀ ( E ↾ 𝐴)
32releqi 5688 . 2 (Rel ∼ 𝐴 ↔ Rel ≀ ( E ↾ 𝐴))
41, 3mpbir 230 1 Rel ∼ 𝐴
Colors of variables: wff setvar class
Syntax hints:   E cep 5494  ccnv 5588  cres 5591  Rel wrel 5594  ccoss 36333  ccoels 36334
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ss 3904  df-opab 5137  df-xp 5595  df-rel 5596  df-coss 36537  df-coels 36538
This theorem is referenced by:  erim2  36789
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