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Definition df-cnvrefrels 38927
Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 38929 (which uses the traditional subclass relation ) : we use converse subset relation (brcnvssr 38907) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23470), symmetric (df-syms 38943) and transitive (df-trs 38977) sets.

We use this concept to define functions (df-funsALTV 39087, df-funALTV 39088) and disjoints (df-disjs 39110, df-disjALTV 39111).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 38937. Alternate definitions are dfcnvrefrels2 38929 and dfcnvrefrels3 38930. (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 38512 . 2 class CnvRefRels
2 ccnvrefs 38511 . . 3 class CnvRefs
3 crels 38506 . . 3 class Rels
42, 3cin 3888 . 2 class ( CnvRefs ∩ Rels )
51, 4wceq 1542 1 wff CnvRefRels = ( CnvRefs ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfcnvrefrels2  38929  dfcnvrefrels3  38930
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