Metamath Proof Explorer


Theorem dvf

Description: The derivative is a function. (Contributed by Mario Carneiro, 8-Aug-2014) (Revised by Mario Carneiro, 9-Feb-2015)

Ref Expression
Assertion dvf ⊢ F ℝ ′ : dom ⁡ F ℝ ′ ⟶ ℂ

Proof

Step Hyp Ref Expression
1 reelprrecn ⊢ ℝ ∈ ℝ ℂ
2 dvfg ⊢ ℝ ∈ ℝ ℂ → F ℝ ′ : dom ⁡ F ℝ ′ ⟶ ℂ
3 1 2 ax-mp ⊢ F ℝ ′ : dom ⁡ F ℝ ′ ⟶ ℂ