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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 ∈ V ↦ { ⟨ 𝑓 , 𝑝 ⟩ ∣ ( 𝑓 ( Trails ‘ 𝑔 ) 𝑝 ∧ 𝑓 : ( 0 ..^ ( ♯ ‘ 𝑓 ) ) –onto→ dom ( iEdg ‘ 𝑔 ) ) } )
2	1	relmptopab	⊢ Rel ( EulerPaths ‘ 𝐺 )