Metamath Proof Explorer


Theorem resincld

Description: Closure of the sine function. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis resincld.1 ⊢ φ → A ∈ ℝ
Assertion resincld ⊢ φ → sin ⁡ A ∈ ℝ

Proof

Step Hyp Ref Expression
1 resincld.1 ⊢ φ → A ∈ ℝ
2 resincl ⊢ A ∈ ℝ → sin ⁡ A ∈ ℝ
3 1 2 syl ⊢ φ → sin ⁡ A ∈ ℝ