Description: Closure of the base set in a uniform limit. (Contributed by Mario Carneiro, 26-Feb-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | ulmscl | |- ( F ( ~~>u ` S ) G -> S e. _V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br | |- ( F ( ~~>u ` S ) G <-> <. F , G >. e. ( ~~>u ` S ) ) |
|
2 | elfvex | |- ( <. F , G >. e. ( ~~>u ` S ) -> S e. _V ) |
|
3 | 1 2 | sylbi | |- ( F ( ~~>u ` S ) G -> S e. _V ) |