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 )