Description: The restriction of the identity relation to a set is a set. (Contributed by AV, 15-Feb-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | resiexd.b | ⊢ ( 𝜑 → 𝐵 ∈ 𝑉 ) | |
Assertion | resiexd | ⊢ ( 𝜑 → ( I ↾ 𝐵 ) ∈ V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resiexd.b | ⊢ ( 𝜑 → 𝐵 ∈ 𝑉 ) | |
2 | funi | ⊢ Fun I | |
3 | resfunexg | ⊢ ( ( Fun I ∧ 𝐵 ∈ 𝑉 ) → ( I ↾ 𝐵 ) ∈ V ) | |
4 | 2 1 3 | sylancr | ⊢ ( 𝜑 → ( I ↾ 𝐵 ) ∈ V ) |