Description: Membership in a closed-below, open-above interval of extended reals. (Contributed by NM, 24-Dec-2006) (Revised by Mario Carneiro, 3-Nov-2013)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | elico1 | |- ( ( A e. RR* /\ B e. RR* ) -> ( C e. ( A [,) B ) <-> ( C e. RR* /\ A <_ C /\ C < B ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-ico | |- [,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x <_ z /\ z < y ) } ) |
|
| 2 | 1 | elixx1 | |- ( ( A e. RR* /\ B e. RR* ) -> ( C e. ( A [,) B ) <-> ( C e. RR* /\ A <_ C /\ C < B ) ) ) |