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Definition df-cnvrefrels 38886
Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 38888 (which uses the traditional subclass relation ) : we use converse subset relation (brcnvssr 38866) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23466), symmetric (df-syms 38902) and transitive (df-trs 38936) sets.

We use this concept to define functions (df-funsALTV 39046, df-funALTV 39047) and disjoints (df-disjs 39069, df-disjALTV 39070).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 38896. Alternate definitions are dfcnvrefrels2 38888 and dfcnvrefrels3 38889. (Contributed by Peter Mazsa, 7-Jul-2019.)

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

Detailed syntax breakdown of Definition df-cnvrefrels
StepHypRef Expression
1 ccnvrefrels 38471 . 2 class CnvRefRels
2 ccnvrefs 38470 . . 3 class CnvRefs
3 crels 38465 . . 3 class Rels
42, 3cin 3902 . 2 class ( CnvRefs ∩ Rels )
51, 4wceq 1542 1 wff CnvRefRels = ( CnvRefs ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfcnvrefrels2  38888  dfcnvrefrels3  38889
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