Step |
Hyp |
Ref |
Expression |
1 |
|
topnpropd.1 |
|- ( ph -> ( Base ` K ) = ( Base ` L ) ) |
2 |
|
topnpropd.2 |
|- ( ph -> ( TopSet ` K ) = ( TopSet ` L ) ) |
3 |
2 1
|
oveq12d |
|- ( ph -> ( ( TopSet ` K ) |`t ( Base ` K ) ) = ( ( TopSet ` L ) |`t ( Base ` L ) ) ) |
4 |
|
eqid |
|- ( Base ` K ) = ( Base ` K ) |
5 |
|
eqid |
|- ( TopSet ` K ) = ( TopSet ` K ) |
6 |
4 5
|
topnval |
|- ( ( TopSet ` K ) |`t ( Base ` K ) ) = ( TopOpen ` K ) |
7 |
|
eqid |
|- ( Base ` L ) = ( Base ` L ) |
8 |
|
eqid |
|- ( TopSet ` L ) = ( TopSet ` L ) |
9 |
7 8
|
topnval |
|- ( ( TopSet ` L ) |`t ( Base ` L ) ) = ( TopOpen ` L ) |
10 |
3 6 9
|
3eqtr3g |
|- ( ph -> ( TopOpen ` K ) = ( TopOpen ` L ) ) |