Metamath Proof Explorer


Theorem elatcv0

Description: A Hilbert lattice element is an atom iff it covers the zero subspace. (Contributed by NM, 26-Jun-2004) (New usage is discouraged.)

Ref Expression
Assertion elatcv0 A C A HAtoms 0 A

Proof

Step Hyp Ref Expression
1 ela A HAtoms A C 0 A
2 1 baib A C A HAtoms 0 A