Theorem qmapex

Description: Quotient map exists if R exists. Type-safety: ensures QMap is an a set under the standard "relation sethood" hypothesis. (Contributed by Peter Mazsa, 12-Feb-2026)

	Ref	Expression
Assertion	qmapex	|- ( R e. V -> QMap R e. _V )

Proof

Step	Hyp	Ref	Expression
1		df-qmap	|- QMap R = ( x e. dom R |-> [ x ] R )
2		dmexg	|- ( R e. V -> dom R e. _V )
3	2	mptexd	|- ( R e. V -> ( x e. dom R |-> [ x ] R ) e. _V )
4	1 3	eqeltrid	|- ( R e. V -> QMap R e. _V )