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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	$⊢ A \in ℋ$
	Assertion	hvnegidi	$⊢ A +_{ℎ} (-1 \cdot_{ℎ} A) = 0_{ℎ}$

Step	Hyp	Ref	Expression
1		hvaddlid.1	$⊢ A \in ℋ$
2		hvnegid	$⊢ A \in ℋ \to A +_{ℎ} (-1 \cdot_{ℎ} A) = 0_{ℎ}$
3	1 2	ax-mp	$⊢ A +_{ℎ} (-1 \cdot_{ℎ} A) = 0_{ℎ}$