Metamath Proof Explorer
Description: TopSet is unaffected by restriction. (Contributed by Mario
Carneiro, 13-Aug-2015)
|
|
Ref |
Expression |
|
Hypotheses |
resstset.1 |
⊢ 𝐻 = ( 𝐺 ↾s 𝐴 ) |
|
|
resstset.2 |
⊢ 𝐽 = ( TopSet ‘ 𝐺 ) |
|
Assertion |
resstset |
⊢ ( 𝐴 ∈ 𝑉 → 𝐽 = ( TopSet ‘ 𝐻 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
resstset.1 |
⊢ 𝐻 = ( 𝐺 ↾s 𝐴 ) |
2 |
|
resstset.2 |
⊢ 𝐽 = ( TopSet ‘ 𝐺 ) |
3 |
|
df-tset |
⊢ TopSet = Slot 9 |
4 |
|
9nn |
⊢ 9 ∈ ℕ |
5 |
|
1lt9 |
⊢ 1 < 9 |
6 |
1 2 3 4 5
|
resslem |
⊢ ( 𝐴 ∈ 𝑉 → 𝐽 = ( TopSet ‘ 𝐻 ) ) |