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Metamath Proof Explorer

Theorem relqmap

Description: Quotient map is a relation. Guarantees that QMap can be composed, restricted, and used in other relation infrastructure (e.g., membership in Disjs , Rels -based typing). (Contributed by Peter Mazsa, 12-Feb-2026)

		Ref	Expression
	Assertion	relqmap	\|- Rel QMap R

Proof

Step	Hyp	Ref	Expression
1		mptrel	\|- Rel ( x e. dom R \|-> [ x ] R )
2		df-qmap	\|- QMap R = ( x e. dom R \|-> [ x ] R )
3	2	releqi	\|- ( Rel QMap R <-> Rel ( x e. dom R \|-> [ x ] R ) )
4	1 3	mpbir	\|- Rel QMap R