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Metamath Proof Explorer

Theorem hv2negi

Description: Two ways to express the negative of a vector. (Contributed by NM, 31-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypothesis hvaddlid.1 ⊢ A ∈ ℋ
Assertion hv2negi ⊢ 0 ℎ - ℎ A = -1 ⋅ ℎ A

Proof

Step Hyp Ref Expression
1 hvaddlid.1 ⊢ A ∈ ℋ
2 hv2neg ⊢ A ∈ ℋ → 0 ℎ - ℎ A = -1 ⋅ ℎ A
3 1 2 ax-mp ⊢ 0 ℎ - ℎ A = -1 ⋅ ℎ A