Description: The union of a set of Hilbert space subsets is smaller than its supremum. (Contributed by NM, 24-Nov-2004) (Revised by Mario Carneiro, 15-May-2014) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | hsupunss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sspwuni | ||
2 | ococss | ||
3 | 1 2 | sylbi | |
4 | hsupval | ||
5 | 3 4 | sseqtrrd |