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 ) |
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 ) |