Description: The indexed union of a set of basic open sets is in the generated topology. (Contributed by Mario Carneiro, 2-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | tgiun | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfiun3g | |
|
2 | 1 | adantl | |
3 | eqid | |
|
4 | 3 | rnmptss | |
5 | eltg3i | |
|
6 | 4 5 | sylan2 | |
7 | 2 6 | eqeltrd | |