Metamath Proof Explorer
Description: Scalar is unaffected by restriction. (Contributed by Mario
Carneiro, 7-Dec-2014)
|
|
Ref |
Expression |
|
Hypotheses |
resssca.1 |
⊢ 𝐻 = ( 𝐺 ↾s 𝐴 ) |
|
|
resssca.2 |
⊢ 𝐹 = ( Scalar ‘ 𝐺 ) |
|
Assertion |
resssca |
⊢ ( 𝐴 ∈ 𝑉 → 𝐹 = ( Scalar ‘ 𝐻 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
resssca.1 |
⊢ 𝐻 = ( 𝐺 ↾s 𝐴 ) |
2 |
|
resssca.2 |
⊢ 𝐹 = ( Scalar ‘ 𝐺 ) |
3 |
|
df-sca |
⊢ Scalar = Slot 5 |
4 |
|
5nn |
⊢ 5 ∈ ℕ |
5 |
|
1lt5 |
⊢ 1 < 5 |
6 |
1 2 3 4 5
|
resslem |
⊢ ( 𝐴 ∈ 𝑉 → 𝐹 = ( Scalar ‘ 𝐻 ) ) |