Theorem elrelsrelim 38015

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

Step	Hyp	Ref	Expression
1		elrelsrel 38014	. 2 ⊢ (𝑅 ∈ Rels → (𝑅 ∈ Rels ↔ Rel 𝑅))
2	1	ibi 266	1 ⊢ (𝑅 ∈ Rels → Rel 𝑅)

Syntax hints:   → wi 4   ∈ wcel 2098  Rel wrel 5677   Rels crels 37706

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-ss 3957  df-pw 4600  df-rel 5679  df-rels 38012

This theorem is referenced by:  elrelscnveq3  38018  elrelscnveq2  38020  dfdisjs5  38239