Metamath Proof Explorer
Description: *r is unaffected by restriction. (Contributed by Mario Carneiro, 9-Oct-2015)
|
|
Ref |
Expression |
|
Hypotheses |
ressmulr.1 |
⊢ 𝑆 = ( 𝑅 ↾s 𝐴 ) |
|
|
ressstarv.2 |
⊢ ∗ = ( *𝑟 ‘ 𝑅 ) |
|
Assertion |
ressstarv |
⊢ ( 𝐴 ∈ 𝑉 → ∗ = ( *𝑟 ‘ 𝑆 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ressmulr.1 |
⊢ 𝑆 = ( 𝑅 ↾s 𝐴 ) |
2 |
|
ressstarv.2 |
⊢ ∗ = ( *𝑟 ‘ 𝑅 ) |
3 |
|
df-starv |
⊢ *𝑟 = Slot 4 |
4 |
|
4nn |
⊢ 4 ∈ ℕ |
5 |
|
1lt4 |
⊢ 1 < 4 |
6 |
1 2 3 4 5
|
resslem |
⊢ ( 𝐴 ∈ 𝑉 → ∗ = ( *𝑟 ‘ 𝑆 ) ) |