Description: The union of a set of closed subspaces is smaller than its supremum. (Contributed by NM, 14-Aug-2002) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | chsupunss | |- ( A C_ CH -> U. A C_ ( \/H ` A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chsspwh | |- CH C_ ~P ~H |
|
2 | sstr | |- ( ( A C_ CH /\ CH C_ ~P ~H ) -> A C_ ~P ~H ) |
|
3 | 1 2 | mpan2 | |- ( A C_ CH -> A C_ ~P ~H ) |
4 | hsupunss | |- ( A C_ ~P ~H -> U. A C_ ( \/H ` A ) ) |
|
5 | 3 4 | syl | |- ( A C_ CH -> U. A C_ ( \/H ` A ) ) |