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Definition df-cnvrefrels 39205
Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 39207 (which uses the traditional subclass relation ) : we use converse subset relation (brcnvssr 39185) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23645), symmetric (df-syms 39221) and transitive (df-trs 39255) sets.

We use this concept to define functions (df-funsALTV 39365, df-funALTV 39366) and disjoints (df-disjs 39388, df-disjALTV 39389).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 39215. Alternate definitions are dfcnvrefrels2 39207 and dfcnvrefrels3 39208. (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 38790 . 2 class CnvRefRels
2 ccnvrefs 38789 . . 3 class CnvRefs
3 crels 38784 . . 3 class Rels
42, 3cin 3912 . 2 class ( CnvRefs ∩ Rels )
51, 4wceq 1568 1 wff CnvRefRels = ( CnvRefs ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfcnvrefrels2  39207  dfcnvrefrels3  39208
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