Theorem qmapeldisjs

Description: When R is a set (e.g., when it is an element of the class of relations df-rels ), the quotient map element of the class of disjoint relations and the disjoint relation predicate for quotient maps are the same. (Contributed by Peter Mazsa, 12-Feb-2026)

	Ref	Expression
Assertion	qmapeldisjs	|- ( R e. V -> ( QMap R e. Disjs <-> Disj QMap R ) )

Proof

Step	Hyp	Ref	Expression
1		qmapex	|- ( R e. V -> QMap R e. _V )
2		eldisjsdisj	|- ( QMap R e. _V -> ( QMap R e. Disjs <-> Disj QMap R ) )
3	1 2	syl	|- ( R e. V -> ( QMap R e. Disjs <-> Disj QMap R ) )