Description: An element of a left-closed right-open interval is less than its upper bound. (Contributed by Glauco Siliprandi, 26-Jun-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | icoltubd.1 | |- ( ph -> A e. RR* ) |
|
icoltubd.2 | |- ( ph -> B e. RR* ) |
||
icoltubd.3 | |- ( ph -> C e. ( A [,) B ) ) |
||
Assertion | icoltubd | |- ( ph -> C < B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | icoltubd.1 | |- ( ph -> A e. RR* ) |
|
2 | icoltubd.2 | |- ( ph -> B e. RR* ) |
|
3 | icoltubd.3 | |- ( ph -> C e. ( A [,) B ) ) |
|
4 | icoltub | |- ( ( A e. RR* /\ B e. RR* /\ C e. ( A [,) B ) ) -> C < B ) |
|
5 | 1 2 3 4 | syl3anc | |- ( ph -> C < B ) |