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 )