Theorem elrelsrelim 38444

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 38443	. 2 ⊢ (𝑅 ∈ Rels → (𝑅 ∈ Rels ↔ Rel 𝑅))
2	1	ibi 267	1 ⊢ (𝑅 ∈ Rels → Rel 𝑅)

Syntax hints:   → wi 4   ∈ wcel 2108  Rel wrel 5705   Rels crels 38137

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-ss 3993  df-pw 4624  df-rel 5707  df-rels 38441

This theorem is referenced by:  elrelscnveq3  38447  elrelscnveq2  38449  dfdisjs5  38668