Theorem opvtxfvi

Description: The set of vertices of a graph represented as an ordered pair of vertices and indexed edges as function value. (Contributed by AV, 4-Mar-2021)

	Ref	Expression
Hypotheses	opvtxfvi.v	⊢ 𝑉 ∈ V
	opvtxfvi.e	⊢ 𝐸 ∈ V
Assertion	opvtxfvi	⊢ ( Vtx ‘ ⟨ 𝑉 , 𝐸 ⟩ ) = 𝑉

Proof

Step	Hyp	Ref	Expression
1		opvtxfvi.v	⊢ 𝑉 ∈ V
2		opvtxfvi.e	⊢ 𝐸 ∈ V
3		opvtxfv	⊢ ( ( 𝑉 ∈ V ∧ 𝐸 ∈ V ) → ( Vtx ‘ ⟨ 𝑉 , 𝐸 ⟩ ) = 𝑉 )
4	1 2 3	mp2an	⊢ ( Vtx ‘ ⟨ 𝑉 , 𝐸 ⟩ ) = 𝑉