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Theorem elrelsrelim 38489
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 38488 . 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 2108  Rel wrel 5690   Rels crels 38184
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ss 3968  df-pw 4602  df-rel 5692  df-rels 38486
This theorem is referenced by:  elrelscnveq3  38492  elrelscnveq2  38494  dfdisjs5  38713
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