Theorem chtcl

Description: Real closure of the Chebyshev function. (Contributed by Mario Carneiro, 15-Sep-2014)

	Ref	Expression
Assertion	chtcl	⊢ ( 𝐴 ∈ ℝ → ( θ ‘ 𝐴 ) ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		chtf	⊢ θ : ℝ ⟶ ℝ
2	1	ffvelrni	⊢ ( 𝐴 ∈ ℝ → ( θ ‘ 𝐴 ) ∈ ℝ )