Theorem hvmulcli

Description: Closure inference for scalar multiplication. (Contributed by NM, 1-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hvmulcl.1	|- A e. CC
	hvmulcl.2	|- B e. ~H
Assertion	hvmulcli	|- ( A .h B ) e. ~H

Proof

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