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Definition df-cnvrefrels 36684
Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 36686 (which uses the traditional subclass relation ) : we use converse subset relation (brcnvssr 36666) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 22701), symmetric (df-syms 36698) and transitive (df-trs 36728) sets.

We use this concept to define functions (df-funsALTV 36834, df-funALTV 36835) and disjoints (df-disjs 36857, df-disjALTV 36858).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 36692. Alternate definitions are dfcnvrefrels2 36686 and dfcnvrefrels3 36687. (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 36385 . 2 class CnvRefRels
2 ccnvrefs 36384 . . 3 class CnvRefs
3 crels 36379 . . 3 class Rels
42, 3cin 3891 . 2 class ( CnvRefs ∩ Rels )
51, 4wceq 1539 1 wff CnvRefRels = ( CnvRefs ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfcnvrefrels2  36686  dfcnvrefrels3  36687
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