Description: Triangle inequality for the distance function of a metric space. (Contributed by NM, 30-Aug-2006) (Revised by Mario Carneiro, 20-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | mettri2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | metxmet | |
|
2 | xmettri2 | |
|
3 | 1 2 | sylan | |
4 | metcl | |
|
5 | 4 | 3adant3r3 | |
6 | metcl | |
|
7 | 6 | 3adant3r2 | |
8 | 5 7 | rexaddd | |
9 | 3 8 | breqtrd | |