Metamath Proof Explorer
Description: .r is unaffected by restriction. (Contributed by Stefan O'Rear, 27-Nov-2014)
|
|
Ref |
Expression |
|
Hypotheses |
ressmulr.1 |
⊢ 𝑆 = ( 𝑅 ↾s 𝐴 ) |
|
|
ressmulr.2 |
⊢ · = ( .r ‘ 𝑅 ) |
|
Assertion |
ressmulr |
⊢ ( 𝐴 ∈ 𝑉 → · = ( .r ‘ 𝑆 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ressmulr.1 |
⊢ 𝑆 = ( 𝑅 ↾s 𝐴 ) |
2 |
|
ressmulr.2 |
⊢ · = ( .r ‘ 𝑅 ) |
3 |
|
df-mulr |
⊢ .r = Slot 3 |
4 |
|
3nn |
⊢ 3 ∈ ℕ |
5 |
|
1lt3 |
⊢ 1 < 3 |
6 |
1 2 3 4 5
|
resslem |
⊢ ( 𝐴 ∈ 𝑉 → · = ( .r ‘ 𝑆 ) ) |