Description: The closed unit interval is a subset of the set of the real numbers. Useful lemma for manipulating probabilities within the closed unit interval. (Contributed by Thierry Arnoux, 21-Dec-2016)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | elunitrn | |- ( A e. ( 0 [,] 1 ) -> A e. RR ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elicc01 | |- ( A e. ( 0 [,] 1 ) <-> ( A e. RR /\ 0 <_ A /\ A <_ 1 ) ) |
|
| 2 | 1 | simp1bi | |- ( A e. ( 0 [,] 1 ) -> A e. RR ) |