Definition df-cnvrefrels 38517

Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 38519 (which uses the traditional subclass relation ⊆) : we use converse subset relation (brcnvssr 38497) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23392), symmetric (df-syms 38533) and transitive (df-trs 38563) sets.

We use this concept to define functions (df-funsALTV 38673, df-funALTV 38674) and disjoints (df-disjs 38696, df-disjALTV 38697).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 38527. Alternate definitions are dfcnvrefrels2 38519 and dfcnvrefrels3 38520. (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 38177	. 2 class CnvRefRels
2		ccnvrefs 38176	. . 3 class CnvRefs
3		crels 38171	. . 3 class Rels
4	2, 3	cin 3913	. 2 class ( CnvRefs ∩ Rels )
5	1, 4	wceq 1540	1 wff CnvRefRels = ( CnvRefs ∩ Rels )

This definition is referenced by:  dfcnvrefrels2  38519  dfcnvrefrels3  38520