Metamath Proof Explorer


Theorem wksv

Description: The class of walks is a set. (Contributed by AV, 15-Jan-2021) (Proof shortened by SN, 11-Dec-2024)

Ref Expression
Assertion wksv { ⟨ 𝑓 , 𝑝 ⟩ ∣ 𝑓 ( Walks ‘ 𝐺 ) 𝑝 } ∈ V

Proof

Step Hyp Ref Expression
1 fvex ( Walks ‘ 𝐺 ) ∈ V
2 opabss { ⟨ 𝑓 , 𝑝 ⟩ ∣ 𝑓 ( Walks ‘ 𝐺 ) 𝑝 } ⊆ ( Walks ‘ 𝐺 )
3 1 2 ssexi { ⟨ 𝑓 , 𝑝 ⟩ ∣ 𝑓 ( Walks ‘ 𝐺 ) 𝑝 } ∈ V