Theorem elrelsrelim 39641

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 39640	. 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 2147  Rel wrel 5663   Rels crels 39383

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-ss 3901  df-pw 4562  df-rel 5665  df-rels 39638

This theorem is used by:  elrelscnveq3  39825  elrelscnveq2  39827  dfdisjs5  39995  eldisjs6  40138