Description: Real closure of an extended metric value that is upper bounded by a real. (Contributed by Thierry Arnoux, 11-Mar-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | psmetlecl | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | psmetcl | |
|
2 | 1 | 3expb | |
3 | 2 | 3adant3 | |
4 | simp3l | |
|
5 | psmetge0 | |
|
6 | 5 | 3expb | |
7 | 6 | 3adant3 | |
8 | simp3r | |
|
9 | xrrege0 | |
|
10 | 3 4 7 8 9 | syl22anc | |