Theorem hvsubcli

Description: Closure of vector subtraction. (Contributed by NM, 2-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hvaddcl.1	$$⊢A\in \mathscr{H}$$
	hvaddcl.2	$$⊢B\in \mathscr{H}$$
Assertion	hvsubcli	$$⊢A{-}_{ℎ}B\in \mathscr{H}$$

Proof

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