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Metamath Proof Explorer

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 ffvelcdmi ⊢ ( 𝐴 ∈ ℝ → ( θ ‘ 𝐴 ) ∈ ℝ )