Theorem opvtxov

Description: The set of vertices 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	opvtxov	⊢ ( ( 𝑉 ∈ 𝑋 ∧ 𝐸 ∈ 𝑌 ) → ( 𝑉 Vtx 𝐸 ) = 𝑉 )

Proof

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