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Metamath Proof Explorer

Theorem releupth

Description: The set ( EulerPathsG ) of all Eulerian paths on G is a set of pairs by our definition of an Eulerian path, and so is a relation. (Contributed by Mario Carneiro, 12-Mar-2015) (Revised by AV, 18-Feb-2021)

		Ref	Expression
	Assertion	releupth	$⊢ Rel EulerPaths (G)$

Proof

Step	Hyp	Ref	Expression
1		df-eupth	$⊢ EulerPaths = (g \in V ⟼ \{⟨f, p⟩ \| (f Trails (g) p \land f : (0 ..^\|f\|) \underset{onto}{⟶} dom iEdg (g))\})$
2	1	relmptopab	$⊢ Rel EulerPaths (G)$