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Theorem elrelsrelim 38469
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 38468 . 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 5693   Rels crels 38163
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-ss 3979  df-pw 4606  df-rel 5695  df-rels 38466
This theorem is referenced by:  elrelscnveq3  38472  elrelscnveq2  38474  dfdisjs5  38693
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