Description: The union of a set of subspaces is smaller than its supremum. (Contributed by NM, 26-Nov-2004) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | shsupunss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | shsspwh | ||
2 | sstr | ||
3 | 1 2 | mpan2 | |
4 | 3 | unissd | |
5 | unipw | ||
6 | 4 5 | sseqtrdi | |
7 | spanss2 | ||
8 | 6 7 | syl |