Metamath Proof Explorer


Theorem addid1d

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

Ref Expression
Hypothesis muld.1 ( 𝜑𝐴 ∈ ℂ )
Assertion addid1d ( 𝜑 → ( 𝐴 + 0 ) = 𝐴 )

Proof

Step Hyp Ref Expression
1 muld.1 ( 𝜑𝐴 ∈ ℂ )
2 addid1 ( 𝐴 ∈ ℂ → ( 𝐴 + 0 ) = 𝐴 )
3 1 2 syl ( 𝜑 → ( 𝐴 + 0 ) = 𝐴 )