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Definition df-cnvrefrels 39458
Description: Define the class of converse reflexive relations. This is practically dfcnvrefrels2 39460 (which uses the traditional subclass relation ) : we use converse subset relation (brcnvssr 39438) here to ensure the comparability to the definitions of the classes of all reflexive (df-ref 23785), symmetric (df-syms 39474) and transitive (df-trs 39508) sets.

We use this concept to define functions (df-funsALTV 39618, df-funALTV 39619) and disjoints (df-disjs 39641, df-disjALTV 39642).

For sets, being an element of the class of converse reflexive relations is equivalent to satisfying the converse reflexive relation predicate, see elcnvrefrelsrel 39468. Alternate definitions are dfcnvrefrels2 39460 and dfcnvrefrels3 39461. (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 39043 . 2 class CnvRefRels
2 ccnvrefs 39042 . . 3 class CnvRefs
3 crels 39037 . . 3 class Rels
42, 3cin 3897 . 2 class ( CnvRefs ∩ Rels )
51, 4wceq 1570 1 wff CnvRefRels = ( CnvRefs ∩ Rels )
Colors of variables:    wff setvar class
This definition is used by:  dfcnvrefrels2  39460  dfcnvrefrels3  39461
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