Theorem shscomi

Description: Commutative law for subspace sum. (Contributed by NM, 17-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	shincl.1	|- A e. SH
	shincl.2	|- B e. SH
Assertion	shscomi	|- ( A +H B ) = ( B +H A )

Proof

Step	Hyp	Ref	Expression
1		shincl.1	|- A e. SH
2		shincl.2	|- B e. SH
3		shscom	|- ( ( A e. SH /\ B e. SH ) -> ( A +H B ) = ( B +H A ) )
4	1 2 3	mp2an	|- ( A +H B ) = ( B +H A )