Theorem elunitge0

Description: An element of the closed unit interval is positive. Useful lemma for manipulating probabilities within the closed unit interval. (Contributed by Thierry Arnoux, 20-Dec-2016)

	Ref	Expression
Assertion	elunitge0	|- ( A e. ( 0 [,] 1 ) -> 0 <_ A )

Proof

Step	Hyp	Ref	Expression
1		elicc01	|- ( A e. ( 0 [,] 1 ) <-> ( A e. RR /\ 0 <_ A /\ A <_ 1 ) )
2	1	simp2bi	|- ( A e. ( 0 [,] 1 ) -> 0 <_ A )