Definition df-cnvrefrels 38510

Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 38512 (which uses the traditional subclass relation ⊆) : we use converse subset relation (brcnvssr 38490) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23425), symmetric (df-syms 38526) and transitive (df-trs 38556) sets.

We use this concept to define functions (df-funsALTV 38666, df-funALTV 38667) and disjoints (df-disjs 38689, df-disjALTV 38690).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 38520. Alternate definitions are dfcnvrefrels2 38512 and dfcnvrefrels3 38513. (Contributed by Peter Mazsa, 7-Jul-2019.)

Assertion

Ref	Expression
df-cnvrefrels	⊢ CnvRefRels = ( CnvRefs ∩ Rels )

Detailed syntax breakdown of Definition df-cnvrefrels

Step	Hyp	Ref	Expression
1		ccnvrefrels 38170	. 2 class CnvRefRels
2		ccnvrefs 38169	. . 3 class CnvRefs
3		crels 38164	. . 3 class Rels
4	2, 3	cin 3910	. 2 class ( CnvRefs ∩ Rels )
5	1, 4	wceq 1540	1 wff CnvRefRels = ( CnvRefs ∩ Rels )

This definition is referenced by:  dfcnvrefrels2  38512  dfcnvrefrels3  38513