Metamath Proof Explorer


Theorem addlidd

Description: 0 is a left identity for addition. (Contributed by Mario Carneiro, 27-May-2016)

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

Proof

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