Theorem atelch

Description: An atom is a Hilbert lattice element. (Contributed by NM, 22-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Assertion	atelch	⊢ ( 𝐴 ∈ HAtoms → 𝐴 ∈ Cℋ )

Proof

Step	Hyp	Ref	Expression
1		atssch	⊢ HAtoms ⊆ Cℋ
2	1	sseli	⊢ ( 𝐴 ∈ HAtoms → 𝐴 ∈ Cℋ )