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Metamath Proof Explorer

Theorem atelch

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

		Ref	Expression
	Assertion	atelch	$⊢ A \in HAtoms \to A \in C_{ℋ}$

Step	Hyp	Ref	Expression
1		atssch	$⊢ HAtoms \subseteq C_{ℋ}$
2	1	sseli	$⊢ A \in HAtoms \to A \in C_{ℋ}$