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Metamath Proof Explorer

Theorem asincl

Description: Closure for the arcsin function. (Contributed by Mario Carneiro, 31-Mar-2015)

Ref Expression
Assertion asincl ( 𝐴 ∈ ℂ → ( arcsin ‘ 𝐴 ) ∈ ℂ )

Proof

Step Hyp Ref Expression
1 asinf ⊢ arcsin : ℂ ⟶ ℂ
2 1 ffvelcdmi ⊢ ( 𝐴 ∈ ℂ → ( arcsin ‘ 𝐴 ) ∈ ℂ )