Metamath Proof Explorer


Theorem elunitcn

Description: The closed unit interval is a subset of the set of the complex numbers. Useful lemma for manipulating probabilities within the closed unit interval. (Contributed by Thierry Arnoux, 21-Dec-2016)

Ref Expression
Assertion elunitcn ⊢ A ∈ 0 1 → A ∈ ℂ

Proof

Step Hyp Ref Expression
1 elunitrn ⊢ A ∈ 0 1 → A ∈ ℝ
2 1 recnd ⊢ A ∈ 0 1 → A ∈ ℂ