Theorem atdmd2

Description: Two Hilbert lattice elements have the dual modular pair property if the second is an atom. (Contributed by NM, 6-Jul-2004) (New usage is discouraged.)

	Ref	Expression
Assertion	atdmd2	|- ( ( A e. CH /\ B e. HAtoms ) -> A MH* B )

Proof

Step	Hyp	Ref	Expression
1		atdmd	|- ( ( B e. HAtoms /\ A e. CH ) -> B MH* A )
2	1	ancoms	|- ( ( A e. CH /\ B e. HAtoms ) -> B MH* A )
3		atelch	|- ( B e. HAtoms -> B e. CH )
4		dmdsym	|- ( ( A e. CH /\ B e. CH ) -> ( A MH* B <-> B MH* A ) )
5	3 4	sylan2	|- ( ( A e. CH /\ B e. HAtoms ) -> ( A MH* B <-> B MH* A ) )
6	2 5	mpbird	|- ( ( A e. CH /\ B e. HAtoms ) -> A MH* B )