Definition df-refrels 38467

Description: Define the class of reflexive relations. This is practically dfrefrels2 38469 (which reveals that RefRels can not include proper classes like I as is elements, see comments of dfrefrels2 38469).

Another alternative definition is dfrefrels3 38470. The element of this class and the reflexive relation predicate (df-refrel 38468) are the same, that is, (𝑅 ∈ RefRels ↔ RefRel 𝑅) when 𝐴 is a set, see elrefrelsrel 38476.

This definition is similar to the definitions of the classes of symmetric (df-symrels 38499) and transitive (df-trrels 38529) 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 38140	. 2 class RefRels
2		crefs 38139	. . 3 class Refs
3		crels 38137	. . 3 class Rels
4	2, 3	cin 3975	. 2 class ( Refs ∩ Rels )
5	1, 4	wceq 1537	1 wff RefRels = ( Refs ∩ Rels )

This definition is referenced by:  dfrefrels2  38469