Theorem elrelsrelim 39092

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 39091	. 2 ⊢ (𝑅 ∈ Rels → (𝑅 ∈ Rels ↔ Rel 𝑅))
2	1	ibi 270	1 ⊢ (𝑅 ∈ Rels → Rel 𝑅)

Syntax hints:   → wi 4   ∈ wcel 2143  Rel wrel 5666   Rels crels 38834

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-ss 3922  df-pw 4564  df-rel 5668  df-rels 39089

This theorem is referenced by:  elrelscnveq3  39276  elrelscnveq2  39278  dfdisjs5  39446  eldisjs6  39589