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Metamath Proof Explorer

Theorem qmapex

Description: Quotient map exists if R exists. Type-safety: ensures QMap is 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	$⊢ R \in V \to dom R \in V$
3	2	mptexd	$⊢ R \in V \to (x \in dom R ⟼ [x] R) \in V$
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 \|-