Theorem hvsubvali

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

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

Proof

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