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Metamath Proof Explorer

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 Could not format assertion : No typesetting found for |- ( R e. V -> ( QMap R e. Disjs <-> Disj QMap R ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 qmapex Could not format ( R e. V -> QMap R e. _V ) : No typesetting found for |- ( R e. V -> QMap R e. _V ) with typecode |-
2 eldisjsdisj Could not format ( QMap R e. _V -> ( QMap R e. Disjs <-> Disj QMap R ) ) : No typesetting found for |- ( QMap R e. _V -> ( QMap R e. Disjs <-> Disj QMap R ) ) with typecode |-
3 1 2 syl Could not format ( R e. V -> ( QMap R e. Disjs <-> Disj QMap R ) ) : No typesetting found for |- ( R e. V -> ( QMap R e. Disjs <-> Disj QMap R ) ) with typecode |-