Theorem hvaddcli

Description: Closure of vector addition. (Contributed by NM, 1-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hvaddcl.1	|- A e. ~H
	hvaddcl.2	|- B e. ~H
Assertion	hvaddcli	|- ( A +h B ) e. ~H

Proof

Step	Hyp	Ref	Expression
1		hvaddcl.1	|- A e. ~H
2		hvaddcl.2	|- B e. ~H
3		hvaddcl	|- ( ( A e. ~H /\ B e. ~H ) -> ( A +h B ) e. ~H )
4	1 2 3	mp2an	|- ( A +h B ) e. ~H