Metamath Proof Explorer


Theorem addridd

Description: 0 is an additive identity. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis muld.1 ⊢ φ → A ∈ ℂ
Assertion addridd ⊢ φ → A + 0 = A

Proof

Step Hyp Ref Expression
1 muld.1 ⊢ φ → A ∈ ℂ
2 addrid ⊢ A ∈ ℂ → A + 0 = A
3 1 2 syl ⊢ φ → A + 0 = A