Theorem hvadd32i

Description: Hilbert vector space commutative/associative law. (Contributed by NM, 18-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hvass.1	|- A e. ~H
	hvass.2	|- B e. ~H
	hvass.3	|- C e. ~H
Assertion	hvadd32i	|- ( ( A +h B ) +h C ) = ( ( A +h C ) +h B )

Proof

Step	Hyp	Ref	Expression
1		hvass.1	|- A e. ~H
2		hvass.2	|- B e. ~H
3		hvass.3	|- C e. ~H
4		hvadd32	|- ( ( A e. ~H /\ B e. ~H /\ C e. ~H ) -> ( ( A +h B ) +h C ) = ( ( A +h C ) +h B ) )
5	1 2 3 4	mp3an	|- ( ( A +h B ) +h C ) = ( ( A +h C ) +h B )