Theorem hvnegidi

Description: Addition of negative of a vector to itself. (Contributed by NM, 18-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Hypothesis	hvaddid2.1	$$⊢A\in \mathscr{H}$$
Assertion	hvnegidi	$$⊢A{+}_{ℎ}\left(-1{\cdot }_{ℎ}A\right)=0_{ℎ}$$

Proof

Step	Hyp	Ref	Expression
1		hvaddid2.1	$$⊢A\in \mathscr{H}$$
2		hvnegid	$$⊢A\in \mathscr{H}\to A{+}_{ℎ}\left(-1{\cdot }_{ℎ}A\right)=0_{ℎ}$$
3	1 2	ax-mp	$$⊢A{+}_{ℎ}\left(-1{\cdot }_{ℎ}A\right)=0_{ℎ}$$