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Metamath Proof Explorer

Theorem dfqmap3

Description: Alternate definition of the quotient map: QMap as ordered-pair class abstraction. Gives the raw set-builder characterization for extensional proofs, Rel proofs ( relqmap ), and composition/intersection manipulations. (Contributed by Peter Mazsa, 14-Feb-2026)

		Ref	Expression
	Assertion	dfqmap3	Could not format assertion : No typesetting found for \|- QMap R = { <. x , y >. \| ( x e. dom R /\ y = [ x ] R ) } 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		df-mpt	$⊢ (x \in dom R ⟼ [x] R) = \{⟨x, y⟩ \| (x \in dom R \land y = [x] R)\}$
3	1 2	eqtri	Could not format QMap R = { <. x , y >. \| ( x e. dom R /\ y = [ x ] R ) } : No typesetting found for \|- QMap R = { <. x , y >. \| ( x e. dom R /\ y = [ x ] R ) } with typecode \|-