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	$$⊢\left(x\in \mathrm{dom}R⟼\left[x\right]R\right)=\left\{⟨x,y⟩|\left(x\in \mathrm{dom}R\wedge y=\left[x\right]R\right)\right\}$$
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 |-