Description: Topology of an opposite group. (Contributed by Mario Carneiro, 17-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | oppgbas.1 | |- O = ( oppG ` R ) |
|
oppgtopn.2 | |- J = ( TopOpen ` R ) |
||
Assertion | oppgtopn | |- J = ( TopOpen ` O ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oppgbas.1 | |- O = ( oppG ` R ) |
|
2 | oppgtopn.2 | |- J = ( TopOpen ` R ) |
|
3 | eqid | |- ( Base ` R ) = ( Base ` R ) |
|
4 | eqid | |- ( TopSet ` R ) = ( TopSet ` R ) |
|
5 | 3 4 | topnval | |- ( ( TopSet ` R ) |`t ( Base ` R ) ) = ( TopOpen ` R ) |
6 | 1 3 | oppgbas | |- ( Base ` R ) = ( Base ` O ) |
7 | 1 4 | oppgtset | |- ( TopSet ` R ) = ( TopSet ` O ) |
8 | 6 7 | topnval | |- ( ( TopSet ` R ) |`t ( Base ` R ) ) = ( TopOpen ` O ) |
9 | 2 5 8 | 3eqtr2i | |- J = ( TopOpen ` O ) |