Theorem hvsubassi

Description: Hilbert vector space associative law for subtraction. (Contributed by NM, 7-Oct-1999) (Revised by Mario Carneiro, 15-May-2014) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hvass.1	|- A e. ~H
	hvass.2	|- B e. ~H
	hvass.3	|- C e. ~H
Assertion	hvsubassi	|- ( ( A -h B ) -h C ) = ( A -h ( B +h C ) )

Proof

Step	Hyp	Ref	Expression
1		hvass.1	|- A e. ~H
2		hvass.2	|- B e. ~H
3		hvass.3	|- C e. ~H
4		hvsubass	|- ( ( A e. ~H /\ B e. ~H /\ C e. ~H ) -> ( ( A -h B ) -h C ) = ( A -h ( B +h C ) ) )
5	1 2 3 4	mp3an	|- ( ( A -h B ) -h C ) = ( A -h ( B +h C ) )