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Metamath Proof Explorer

Theorem hvnegidi

Description: Addition of negative of a vector to itself. (Contributed by NM, 18-Aug-1999) (New usage is discouraged.)

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

Proof

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