Description: The uniform structure generated by metric D is a uniform structure. (Contributed by Thierry Arnoux, 1-Dec-2017) (Revised by Thierry Arnoux, 11-Feb-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | metuust | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | metuval | |
|
2 | 1 | adantl | |
3 | oveq2 | |
|
4 | 3 | imaeq2d | |
5 | 4 | cbvmptv | |
6 | 5 | rneqi | |
7 | 6 | metust | |
8 | 2 7 | eqeltrd | |