Theorem resexd

Description: The restriction of a set is a set. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypothesis	resexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
Assertion	resexd	⊢ ( 𝜑 → ( 𝐴 ↾ 𝐵 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		resexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		resexg	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ↾ 𝐵 ) ∈ V )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ↾ 𝐵 ) ∈ V )