Theorem opiedgov

Description: The set of indexed edges of a graph represented as an ordered pair of vertices and indexed edges as operation value. (Contributed by AV, 21-Sep-2020)

	Ref	Expression
Assertion	opiedgov	⊢ ( ( 𝑉 ∈ 𝑋 ∧ 𝐸 ∈ 𝑌 ) → ( 𝑉 iEdg 𝐸 ) = 𝐸 )

Proof

Step	Hyp	Ref	Expression
1		df-ov	⊢ ( 𝑉 iEdg 𝐸 ) = ( iEdg ‘ ⟨ 𝑉 , 𝐸 ⟩ )
2		opiedgfv	⊢ ( ( 𝑉 ∈ 𝑋 ∧ 𝐸 ∈ 𝑌 ) → ( iEdg ‘ ⟨ 𝑉 , 𝐸 ⟩ ) = 𝐸 )
3	1 2	syl5eq	⊢ ( ( 𝑉 ∈ 𝑋 ∧ 𝐸 ∈ 𝑌 ) → ( 𝑉 iEdg 𝐸 ) = 𝐸 )