Definition df-refrels 38512

Description: Define the class of reflexive relations. This is practically dfrefrels2 38514 (which reveals that RefRels can not include proper classes like I as is elements, see comments of dfrefrels2 38514).

Another alternative definition is dfrefrels3 38515. The element of this class and the reflexive relation predicate (df-refrel 38513) are the same, that is, (𝑅 ∈ RefRels ↔ RefRel 𝑅) when 𝐴 is a set, see elrefrelsrel 38521.

This definition is similar to the definitions of the classes of symmetric (df-symrels 38544) and transitive (df-trrels 38574) 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 38187	. 2 class RefRels
2		crefs 38186	. . 3 class Refs
3		crels 38184	. . 3 class Rels
4	2, 3	cin 3950	. 2 class ( Refs ∩ Rels )
5	1, 4	wceq 1540	1 wff RefRels = ( Refs ∩ Rels )

This definition is referenced by:  dfrefrels2  38514