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Definition df-cnvrefrels 38002
Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 38004 (which uses the traditional subclass relation ) : we use converse subset relation (brcnvssr 37982) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23427), symmetric (df-syms 38018) and transitive (df-trs 38048) sets.

We use this concept to define functions (df-funsALTV 38157, df-funALTV 38158) and disjoints (df-disjs 38180, df-disjALTV 38181).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 38012. Alternate definitions are dfcnvrefrels2 38004 and dfcnvrefrels3 38005. (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 37661 . 2 class CnvRefRels
2 ccnvrefs 37660 . . 3 class CnvRefs
3 crels 37655 . . 3 class Rels
42, 3cin 3946 . 2 class ( CnvRefs ∩ Rels )
51, 4wceq 1533 1 wff CnvRefRels = ( CnvRefs ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfcnvrefrels2  38004  dfcnvrefrels3  38005
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