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Definition df-cnvrefrels 37396
Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 37398 (which uses the traditional subclass relation ) : we use converse subset relation (brcnvssr 37376) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23009), symmetric (df-syms 37412) and transitive (df-trs 37442) sets.

We use this concept to define functions (df-funsALTV 37551, df-funALTV 37552) and disjoints (df-disjs 37574, df-disjALTV 37575).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 37406. Alternate definitions are dfcnvrefrels2 37398 and dfcnvrefrels3 37399. (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 37051 . 2 class CnvRefRels
2 ccnvrefs 37050 . . 3 class CnvRefs
3 crels 37045 . . 3 class Rels
42, 3cin 3948 . 2 class ( CnvRefs ∩ Rels )
51, 4wceq 1542 1 wff CnvRefRels = ( CnvRefs ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfcnvrefrels2  37398  dfcnvrefrels3  37399
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