Theorem atelch

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

	Ref	Expression
Assertion	atelch	$$⊢A\in \mathrm{HAtoms}\to A\in {\mathbf{C}}_{\mathscr{H}}$$

Proof

Step	Hyp	Ref	Expression
1		atssch	$$⊢\mathrm{HAtoms}\subseteq {\mathbf{C}}_{\mathscr{H}}$$
2	1	sseli	$$⊢A\in \mathrm{HAtoms}\to A\in {\mathbf{C}}_{\mathscr{H}}$$