Definition df-refrels 36556

Description: Define the class of reflexive relations. This is practically dfrefrels2 36558 (which reveals that RefRels can not include proper classes like I as is elements, see comments of dfrefrels2 36558).

Another alternative definition is dfrefrels3 36559. The element of this class and the reflexive relation predicate (df-refrel 36557) are the same, that is, (𝑅 ∈ RefRels ↔ RefRel 𝑅) when 𝐴 is a set, see elrefrelsrel 36564.

This definition is similar to the definitions of the classes of symmetric (df-symrels 36584) and transitive (df-trrels 36614) relations. (Contributed by Peter Mazsa, 7-Jul-2019.)

Assertion

Ref	Expression
df-refrels	⊢ RefRels = ( Refs ∩ Rels )

Detailed syntax breakdown of Definition df-refrels

Step	Hyp	Ref	Expression
1		crefrels 36265	. 2 class RefRels
2		crefs 36264	. . 3 class Refs
3		crels 36262	. . 3 class Rels
4	2, 3	cin 3882	. 2 class ( Refs ∩ Rels )
5	1, 4	wceq 1539	1 wff RefRels = ( Refs ∩ Rels )

This definition is referenced by:  dfrefrels2  36558