Theorem elrelsrelim 36533

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 36532	. 2 ⊢ (𝑅 ∈ Rels → (𝑅 ∈ Rels ↔ Rel 𝑅))
2	1	ibi 266	1 ⊢ (𝑅 ∈ Rels → Rel 𝑅)

Syntax hints:   → wi 4   ∈ wcel 2108  Rel wrel 5585   Rels crels 36262

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-pw 4532  df-rel 5587  df-rels 36530

This theorem is referenced by:  elrelscnveq3  36536  elrelscnveq2  36538  dfdisjs5  36750