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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 ( 0ℎ −ℎ 𝐴 ) = ( - 1 ·ℎ 𝐴 )

Proof

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