Description: Triangle inequality for the distance function of a pseudometric space. (Contributed by Thierry Arnoux, 11-Feb-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | psmettri | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl | |
|
2 | simpr3 | |
|
3 | simpr1 | |
|
4 | simpr2 | |
|
5 | psmettri2 | |
|
6 | 1 2 3 4 5 | syl13anc | |
7 | psmetsym | |
|
8 | 1 2 3 7 | syl3anc | |
9 | 8 | oveq1d | |
10 | 6 9 | breqtrd | |