Definition df-cnvrefrels 38490

Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 38492 (which uses the traditional subclass relation ⊆) : we use converse subset relation (brcnvssr 38470) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23441), symmetric (df-syms 38506) and transitive (df-trs 38536) sets.

We use this concept to define functions (df-funsALTV 38645, df-funALTV 38646) and disjoints (df-disjs 38668, df-disjALTV 38669).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 38500. Alternate definitions are dfcnvrefrels2 38492 and dfcnvrefrels3 38493. (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 38153	. 2 class CnvRefRels
2		ccnvrefs 38152	. . 3 class CnvRefs
3		crels 38147	. . 3 class Rels
4	2, 3	cin 3925	. 2 class ( CnvRefs ∩ Rels )
5	1, 4	wceq 1540	1 wff CnvRefRels = ( CnvRefs ∩ Rels )

This definition is referenced by:  dfcnvrefrels2  38492  dfcnvrefrels3  38493