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