Description: The absolute value metric is an extended metric. (Contributed by Mario Carneiro, 28-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | remet.1 | |- D = ( ( abs o. - ) |` ( RR X. RR ) ) |
|
Assertion | rexmet | |- D e. ( *Met ` RR ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | remet.1 | |- D = ( ( abs o. - ) |` ( RR X. RR ) ) |
|
2 | 1 | remet | |- D e. ( Met ` RR ) |
3 | metxmet | |- ( D e. ( Met ` RR ) -> D e. ( *Met ` RR ) ) |
|
4 | 2 3 | ax-mp | |- D e. ( *Met ` RR ) |