Metamath Proof Explorer


Theorem 2timesd

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

Ref Expression
Hypothesis 2timesd.1 ⊢ φ → A ∈ ℂ
Assertion 2timesd ⊢ φ → 2 ⁢ A = A + A

Proof

Step Hyp Ref Expression
1 2timesd.1 ⊢ φ → A ∈ ℂ
2 2times ⊢ A ∈ ℂ → 2 ⁢ A = A + A
3 1 2 syl ⊢ φ → 2 ⁢ A = A + A