Theorem hvsubvali

Description: Value of vector subtraction definition. (Contributed by NM, 3-Sep-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hvaddcl.1	$$⊢A\in \mathscr{H}$$
	hvaddcl.2	$$⊢B\in \mathscr{H}$$
Assertion	hvsubvali	$$⊢A{-}_{ℎ}B=A{+}_{ℎ}\left(-1{\cdot }_{ℎ}B\right)$$

Proof

Step	Hyp	Ref	Expression
1		hvaddcl.1	$$⊢A\in \mathscr{H}$$
2		hvaddcl.2	$$⊢B\in \mathscr{H}$$
3		hvsubval	$$⊢\left(A\in \mathscr{H}\wedge B\in \mathscr{H}\right)\to A{-}_{ℎ}B=A{+}_{ℎ}\left(-1{\cdot }_{ℎ}B\right)$$
4	1 2 3	mp2an	$$⊢A{-}_{ℎ}B=A{+}_{ℎ}\left(-1{\cdot }_{ℎ}B\right)$$