Theorem hvaddcl

Description: Closure of vector addition. (Contributed by NM, 18-Apr-2007) (New usage is discouraged.)

	Ref	Expression
Assertion	hvaddcl	$$⊢\left(A\in \mathscr{H}\wedge B\in \mathscr{H}\right)\to A{+}_{ℎ}B\in \mathscr{H}$$

Proof

Step	Hyp	Ref	Expression
1		ax-hfvadd	$$⊢{+}_{ℎ}:\mathscr{H}\times \mathscr{H}⟶\mathscr{H}$$
2	1	fovcl	$$⊢\left(A\in \mathscr{H}\wedge B\in \mathscr{H}\right)\to A{+}_{ℎ}B\in \mathscr{H}$$