Metamath Proof Explorer


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 ≤ 𝐴𝐴 ≤ 1 ) )
2 1 simp1bi ( 𝐴 ∈ ( 0 [,] 1 ) → 𝐴 ∈ ℝ )