Theorem elrelsrelim 39191

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 39190	. 2 ⊢ (𝑅 ∈ Rels → (𝑅 ∈ Rels ↔ Rel 𝑅))
2	1	ibi 270	1 ⊢ (𝑅 ∈ Rels → Rel 𝑅)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2145  Rel wrel 5660   Rels crels 38933

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-ss 3916  df-pw 4559  df-rel 5662  df-rels 39188

This theorem is used by:  elrelscnveq3  39375  elrelscnveq2  39377  dfdisjs5  39545  eldisjs6  39688