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

Proof

Step	Hyp	Ref	Expression
1		df-qmap	Could not format QMap R = ( x e. dom R |-> [ x ] R ) : No typesetting found for |- QMap R = ( x e. dom R |-> [ x ] R ) with typecode |-
2		dmexg	$$⊢R\in V\to \mathrm{dom}R\in \mathrm{V}$$
3	2	mptexd	$$⊢R\in V\to \left(x\in \mathrm{dom}R⟼\left[x\right]R\right)\in \mathrm{V}$$
4	1 3	eqeltrid	Could not format ( R e. V -> QMap R e. _V ) : No typesetting found for |- ( R e. V -> QMap R e. _V ) with typecode |-