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