Description: Given a topology on a set, restricting it to that same set has no effect. (Contributed by Jim Kingdon, 6-Jul-2022)
Ref | Expression | ||
---|---|---|---|
Hypothesis | toponrestid.t | |- A e. ( TopOn ` B ) |
|
Assertion | toponrestid | |- A = ( A |`t B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | toponrestid.t | |- A e. ( TopOn ` B ) |
|
2 | 1 | toponunii | |- B = U. A |
3 | 2 | restid | |- ( A e. ( TopOn ` B ) -> ( A |`t B ) = A ) |
4 | 1 3 | ax-mp | |- ( A |`t B ) = A |
5 | 4 | eqcomi | |- A = ( A |`t B ) |