Theorem elunitrn

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 ∈ ( 0 [,] 1 ) → 𝐴 ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		elicc01	⊢ ( 𝐴 ∈ ( 0 [,] 1 ) ↔ ( 𝐴 ∈ ℝ ∧ 0 ≤ 𝐴 ∧ 𝐴 ≤ 1 ) )
2	1	simp1bi	⊢ ( 𝐴 ∈ ( 0 [,] 1 ) → 𝐴 ∈ ℝ )