Metamath Proof Explorer


Theorem times2d

Description: A number times 2. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis 2timesd.1 ( 𝜑𝐴 ∈ ℂ )
Assertion times2d ( 𝜑 → ( 𝐴 · 2 ) = ( 𝐴 + 𝐴 ) )

Proof

Step Hyp Ref Expression
1 2timesd.1 ( 𝜑𝐴 ∈ ℂ )
2 times2 ( 𝐴 ∈ ℂ → ( 𝐴 · 2 ) = ( 𝐴 + 𝐴 ) )
3 1 2 syl ( 𝜑 → ( 𝐴 · 2 ) = ( 𝐴 + 𝐴 ) )