Description: A member of a set of extended reals is less than or equal to the set's supremum. (Contributed by NM, 7-Feb-2006)
Ref | Expression | ||
---|---|---|---|
Assertion | supxrub | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel2 | |
|
2 | supxrcl | |
|
3 | 2 | adantr | |
4 | xrltso | |
|
5 | 4 | a1i | |
6 | xrsupss | |
|
7 | 5 6 | supub | |
8 | 7 | imp | |
9 | 1 3 8 | xrnltled | |