Theorem struct2grstr

Description: A graph represented as an extensible structure with vertices as base set and indexed edges is actually an extensible structure. (Contributed by AV, 23-Nov-2020)

	Ref	Expression
Hypothesis	struct2grvtx.g	⊢ 𝐺 = { ⟨ ( Base ‘ ndx ) , 𝑉 ⟩ , ⟨ ( .ef ‘ ndx ) , 𝐸 ⟩ }
Assertion	struct2grstr	⊢ 𝐺 Struct ⟨ ( Base ‘ ndx ) , ( .ef ‘ ndx ) ⟩

Proof

Step	Hyp	Ref	Expression
1		struct2grvtx.g	⊢ 𝐺 = { ⟨ ( Base ‘ ndx ) , 𝑉 ⟩ , ⟨ ( .ef ‘ ndx ) , 𝐸 ⟩ }
2		basendxltedgfndx	⊢ ( Base ‘ ndx ) < ( .ef ‘ ndx )
3		edgfndxnn	⊢ ( .ef ‘ ndx ) ∈ ℕ
4	1 2 3	2strstr1	⊢ 𝐺 Struct ⟨ ( Base ‘ ndx ) , ( .ef ‘ ndx ) ⟩