Theorem atssch 32290

Description: Atoms are a subset of the Hilbert lattice. (Contributed by NM, 14-Aug-2002.) (New usage is discouraged.)

Assertion

Ref	Expression
atssch	⊢ HAtoms ⊆ Cℋ

Proof of Theorem atssch

Dummy variable 𝑥 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-at 32285	. 2 ⊢ HAtoms = {𝑥 ∈ Cℋ ∣ 0ℋ ⋖ℋ 𝑥}
2	1	ssrab3 4062	1 ⊢ HAtoms ⊆ Cℋ

Syntax hints:   ⊆ wss 3931   class class class wbr 5123   C_ℋ cch 30876  0_ℋc0h 30882   ⋖_ℋ ccv 30911  HAtomscat 30912

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-rab 3420  df-ss 3948  df-at 32285

This theorem is referenced by:  atelch  32291  shatomistici  32308  hatomistici  32309  chpssati  32310