Theorem subgrv

Description: If a class is a subgraph of another class, both classes are sets. (Contributed by AV, 16-Nov-2020)

	Ref	Expression
Assertion	subgrv	⊢ ( 𝑆 SubGraph 𝐺 → ( 𝑆 ∈ V ∧ 𝐺 ∈ V ) )

Proof

Step	Hyp	Ref	Expression
1		relsubgr	⊢ Rel SubGraph
2	1	brrelex12i	⊢ ( 𝑆 SubGraph 𝐺 → ( 𝑆 ∈ V ∧ 𝐺 ∈ V ) )