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

Step	Hyp	Ref	Expression
1		elrelsrel 37821	. 2 ⊢ (𝑅 ∈ Rels → (𝑅 ∈ Rels ↔ Rel 𝑅))
2	1	ibi 267	1 ⊢ (𝑅 ∈ Rels → Rel 𝑅)

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