Definition df-refrels 37467

Description: Define the class of reflexive relations. This is practically dfrefrels2 37469 (which reveals that RefRels can not include proper classes like I as is elements, see comments of dfrefrels2 37469).

Another alternative definition is dfrefrels3 37470. The element of this class and the reflexive relation predicate (df-refrel 37468) are the same, that is, (𝑅 ∈ RefRels ↔ RefRel 𝑅) when 𝐴 is a set, see elrefrelsrel 37476.

This definition is similar to the definitions of the classes of symmetric (df-symrels 37499) and transitive (df-trrels 37529) 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 37134	. 2 class RefRels
2		crefs 37133	. . 3 class Refs
3		crels 37131	. . 3 class Rels
4	2, 3	cin 3947	. 2 class ( Refs ∩ Rels )
5	1, 4	wceq 1541	1 wff RefRels = ( Refs ∩ Rels )

This definition is referenced by:  dfrefrels2  37469