Definition df-cnvrefrels 38809

Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 38811 (which uses the traditional subclass relation ⊆) : we use converse subset relation (brcnvssr 38789) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23453), symmetric (df-syms 38825) and transitive (df-trs 38859) sets.

We use this concept to define functions (df-funsALTV 38969, df-funALTV 38970) and disjoints (df-disjs 38992, df-disjALTV 38993).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 38819. Alternate definitions are dfcnvrefrels2 38811 and dfcnvrefrels3 38812. (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 38394	. 2 class CnvRefRels
2		ccnvrefs 38393	. . 3 class CnvRefs
3		crels 38388	. . 3 class Rels
4	2, 3	cin 3901	. 2 class ( CnvRefs ∩ Rels )
5	1, 4	wceq 1542	1 wff CnvRefRels = ( CnvRefs ∩ Rels )

This definition is referenced by:  dfcnvrefrels2  38811  dfcnvrefrels3  38812