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Theorem elrelsrelim 37822
Description: The element of the relations class is a relation. (Contributed by Peter Mazsa, 20-Jul-2019.)
Assertion
Ref Expression
elrelsrelim (𝑅 ∈ Rels → Rel 𝑅)

Proof of Theorem elrelsrelim
StepHypRef Expression
1 elrelsrel 37821 . 2 (𝑅 ∈ Rels → (𝑅 ∈ Rels ↔ Rel 𝑅))
21ibi 267 1 (𝑅 ∈ Rels → Rel 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105  Rel wrel 5681   Rels crels 37509
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3475  df-in 3955  df-ss 3965  df-pw 4604  df-rel 5683  df-rels 37819
This theorem is referenced by:  elrelscnveq3  37825  elrelscnveq2  37827  dfdisjs5  38046
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