Description: Membership in an open-below, closed-above interval of extended reals. (Contributed by NM, 24-Dec-2006) (Revised by Mario Carneiro, 3-Nov-2013)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | elioc1 | |- ( ( A e. RR* /\ B e. RR* ) -> ( C e. ( A (,] B ) <-> ( C e. RR* /\ A < C /\ C <_ B ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-ioc | |- (,] = ( 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 ) ) ) |