Metamath Proof Explorer


Theorem hvaddlidi

Description: Addition with the zero vector. (Contributed by NM, 18-Aug-1999) (New usage is discouraged.)

Ref Expression
Hypothesis hvaddlid.1 ⊢ 𝐴 ∈ ℋ
Assertion hvaddlidi ( 0ℎ +ℎ 𝐴 ) = 𝐴

Proof

Step Hyp Ref Expression
1 hvaddlid.1 ⊢ 𝐴 ∈ ℋ
2 hvaddlid ⊢ ( 𝐴 ∈ ℋ → ( 0ℎ +ℎ 𝐴 ) = 𝐴 )
3 1 2 ax-mp ⊢ ( 0ℎ +ℎ 𝐴 ) = 𝐴