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 ∈ ( 0 [,] 1 ) → 0 ≤ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		elicc01	⊢ ( 𝐴 ∈ ( 0 [,] 1 ) ↔ ( 𝐴 ∈ ℝ ∧ 0 ≤ 𝐴 ∧ 𝐴 ≤ 1 ) )
2	1	simp2bi	⊢ ( 𝐴 ∈ ( 0 [,] 1 ) → 0 ≤ 𝐴 )