Definition df-cnvrefrels 38527

Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 38529 (which uses the traditional subclass relation ⊆) : we use converse subset relation (brcnvssr 38507) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23513), symmetric (df-syms 38543) and transitive (df-trs 38573) sets.

We use this concept to define functions (df-funsALTV 38682, df-funALTV 38683) and disjoints (df-disjs 38705, df-disjALTV 38706).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 38537. Alternate definitions are dfcnvrefrels2 38529 and dfcnvrefrels3 38530. (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 38190	. 2 class CnvRefRels
2		ccnvrefs 38189	. . 3 class CnvRefs
3		crels 38184	. . 3 class Rels
4	2, 3	cin 3950	. 2 class ( CnvRefs ∩ Rels )
5	1, 4	wceq 1540	1 wff CnvRefRels = ( CnvRefs ∩ Rels )

This definition is referenced by:  dfcnvrefrels2  38529  dfcnvrefrels3  38530