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Metamath Proof Explorer

Theorem chpcl

Description: Closure for the second Chebyshev function. (Contributed by Mario Carneiro, 7-Apr-2016)

Ref Expression
Assertion chpcl ( 𝐴 ∈ ℝ → ( ψ ‘ 𝐴 ) ∈ ℝ )

Proof

Step Hyp Ref Expression
1 chpf ⊢ ψ : ℝ ⟶ ℝ
2 1 ffvelcdmi ⊢ ( 𝐴 ∈ ℝ → ( ψ ‘ 𝐴 ) ∈ ℝ )