Theorem ela

Description: Atoms in a Hilbert lattice are the elements that cover the zero subspace. Definition of atom in Kalmbach p. 15. (Contributed by NM, 9-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Assertion	ela	|- ( A e. HAtoms <-> ( A e. CH /\ 0H

Proof

Step	Hyp	Ref	Expression
1		breq2	|- ( x = A -> ( 0H 0H
2		df-at	|- HAtoms = { x e. CH | 0H
3	1 2	elrab2	|- ( A e. HAtoms <-> ( A e. CH /\ 0H