Metamath Proof Explorer
Description: Topology of an opposite group. (Contributed by Mario Carneiro, 17-Sep-2015)
|
|
Ref |
Expression |
|
Hypotheses |
oppgbas.1 |
⊢ 𝑂 = ( oppg ‘ 𝑅 ) |
|
|
oppgtset.2 |
⊢ 𝐽 = ( TopSet ‘ 𝑅 ) |
|
Assertion |
oppgtset |
⊢ 𝐽 = ( TopSet ‘ 𝑂 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
oppgbas.1 |
⊢ 𝑂 = ( oppg ‘ 𝑅 ) |
2 |
|
oppgtset.2 |
⊢ 𝐽 = ( TopSet ‘ 𝑅 ) |
3 |
|
df-tset |
⊢ TopSet = Slot 9 |
4 |
|
9nn |
⊢ 9 ∈ ℕ |
5 |
|
2re |
⊢ 2 ∈ ℝ |
6 |
|
2lt9 |
⊢ 2 < 9 |
7 |
5 6
|
gtneii |
⊢ 9 ≠ 2 |
8 |
1 3 4 7
|
oppglem |
⊢ ( TopSet ‘ 𝑅 ) = ( TopSet ‘ 𝑂 ) |
9 |
2 8
|
eqtri |
⊢ 𝐽 = ( TopSet ‘ 𝑂 ) |